70 results found for "completing-square" in Class 10.
Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(7x^2-14x+19=0\) में पूर्ण वर्ग रूप कौनसा सही है?
Which completed square form is correct for \(7x^2-14x+19=0\)?
#quadratic
#completing-square
#no-real-roots
A (7(x-1)2 +12=0)
B (7(x+1)2 +12=0)
C (7(x-1)2 -12=0)
D (7(x-2)2 +19=0)
Explanation opens after your attempt
Correct Answer
A. (7(x-1)2 +12=0)
Step 1
Concept
(7x-2 -14x+19=7(x-1)2 +12), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. (7(x-1)2 +12=0). (7x-2 -14x+19=7(x-1)2 +12), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 3
Exam Tip
(7x-2 -14x+19=7(x-1)2 +12), इसलिए यह वास्तविक (x) के लिए शून्य नहीं हो सकता। परीक्षा में पूर्ण वर्ग रूप से भी मूलों की प्रकृति दिखती है।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(x^2+14x+10=0\) के मूल क्या हैं?
What are the roots of \(x^2+14x+10=0\)?
#quadratic
#completing-square
#roots
A \(x=-7\pm\sqrt{39}\)
B \(x=7\pm\sqrt{39}\)
C \(x=-14\pm\sqrt{39}\)
D \(x=-7\pm39\)
Explanation opens after your attempt
Correct Answer
A. \(x=-7\pm\sqrt{39}\)
Step 1
Concept
Since ((x+7)2 =39), \(x=-7\pm\sqrt{39}\). In exams, write both values using \(\pm\).
Step 2
Why this answer is correct
The correct answer is A. \(x=-7\pm\sqrt{39}\). Since ((x+7)2 =39), \(x=-7\pm\sqrt{39}\). In exams, write both values using \(\pm\).
Step 3
Exam Tip
((x+7)2 =39), इसलिए \(x=-7\pm\sqrt{39}\) है। परीक्षा में \(\pm\) के दोनों मान लिखें।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि \(x^2+14x+10=0\), तो पूर्ण वर्ग विधि से सही रूप कौनसा है?
If \(x^2+14x+10=0\), which form is correct by completing square?
#quadratic
#completing-square
#irrational-roots
A ((x+7)2 =39)
B ((x-7)2 =39)
C ((x+14)2 =10)
D ((x+7)2 =10)
Explanation opens after your attempt
Correct Answer
A. ((x+7)2 =39)
Step 1
Concept
Adding (49) to \(x^2+14x=-10\) gives ((x+7)2 =39). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x+7)2 =39). Adding (49) to \(x^2+14x=-10\) gives ((x+7)2 =39). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2+14x=-10\) में (49) जोड़ने पर ((x+7)2 =39) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(13x^2-52x+9=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?
What roots are obtained for \(13x^2-52x+9=0\) by completing square method?
#quadratic
#completing-square
#irrational-roots
A \(x=2\pm\frac{\sqrt{559}}{13}\)
B \(x=-2\pm\frac{\sqrt{559}}{13}\)
C \(x=4\pm\sqrt{559}\)
D \(x=2\pm\frac{\sqrt{43}}{13}\)
Explanation opens after your attempt
Correct Answer
A. \(x=2\pm\frac{\sqrt{559}}{13}\)
Step 1
Concept
Since ((x-2)2 =\frac{43}{13}), \(x=2\pm\sqrt{\frac{43}{13}}=2\pm\frac{\sqrt{559}}{13}\). In exams, rationalize the denominator.
Step 2
Why this answer is correct
The correct answer is A. \(x=2\pm\frac{\sqrt{559}}{13}\). Since ((x-2)2 =\frac{43}{13}), \(x=2\pm\sqrt{\frac{43}{13}}=2\pm\frac{\sqrt{559}}{13}\). In exams, rationalize the denominator.
Step 3
Exam Tip
((x-2)2 =\frac{43}{13}), इसलिए \(x=2\pm\sqrt{\frac{43}{13}}=2\pm\frac{\sqrt{559}}{13}\) है। परीक्षा में हर को परिमेय बनाएं।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(13x^2-52x+9=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(13x^2-52x+9=0\) by completing the square?
#quadratic
#completing-square
#expert
A ((x-2)2 =\frac{43}{13})
B ((x+2)2 =\frac{43}{13})
C ((x-4)2 =\frac{9}{13})
D ((x-2)2 =4)
Explanation opens after your attempt
Correct Answer
A. ((x-2)2 =\frac{43}{13})
Step 1
Concept
First \(x^2-4x+\frac{9}{13}=0\) is obtained, then ((x-2)2 =\frac{43}{13}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. ((x-2)2 =\frac{43}{13}). First \(x^2-4x+\frac{9}{13}=0\) is obtained, then ((x-2)2 =\frac{43}{13}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2-4x+\frac{9}{13}=0\) बनता है, फिर ((x-2)2 =\frac{43}{13}) मिलता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि \(3x^2+18x+5=0\) को पूर्ण वर्ग विधि से हल किया जाए, तो सही मध्य चरण कौनसा है?
If \(3x^2+18x+5=0\) is solved by completing the square, which middle step is correct?
#quadratic
#completing-square
#expert
A ((x+3)2 =\frac{22}{3})
B ((x-3)2 =\frac{22}{3})
C ((x+6)2 =\frac{5}{3})
D ((x+3)2 =9)
Explanation opens after your attempt
Correct Answer
A. ((x+3)2 =\frac{22}{3})
Step 1
Concept
First \(x^2+6x+\frac{5}{3}=0\) is obtained, then adding (9) gives ((x+3)2 =\frac{22}{3}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. ((x+3)2 =\frac{22}{3}). First \(x^2+6x+\frac{5}{3}=0\) is obtained, then adding (9) gives ((x+3)2 =\frac{22}{3}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2+6x+\frac{5}{3}=0\) मिलता है, फिर (9) जोड़ने पर ((x+3)2 =\frac{22}{3}) बनता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(6x^2-12x+17=0\) में पूर्ण वर्ग रूप कौनसा सही है?
Which completed square form is correct for \(6x^2-12x+17=0\)?
#quadratic
#completing-square
#no-real-roots
A (6(x-1)2 +11=0)
B (6(x+1)2 +11=0)
C (6(x-1)2 -11=0)
D (6(x-2)2 +17=0)
Explanation opens after your attempt
Correct Answer
A. (6(x-1)2 +11=0)
Step 1
Concept
(6x-2 -12x+17=6(x-1)2 +11), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. (6(x-1)2 +11=0). (6x-2 -12x+17=6(x-1)2 +11), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 3
Exam Tip
(6x-2 -12x+17=6(x-1)2 +11), इसलिए यह वास्तविक (x) के लिए शून्य नहीं हो सकता। परीक्षा में पूर्ण वर्ग रूप से भी मूलों की प्रकृति दिखती है।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(x^2+12x+8=0\) के मूल क्या हैं?
What are the roots of \(x^2+12x+8=0\)?
#quadratic
#completing-square
#roots
A \(x=-6\pm2\sqrt{7}\)
B \(x=6\pm2\sqrt{7}\)
C \(x=-12\pm2\sqrt{7}\)
D \(x=-6\pm28\)
Explanation opens after your attempt
Correct Answer
A. \(x=-6\pm2\sqrt{7}\)
Step 1
Concept
Since ((x+6)2 =28), \(x=-6\pm2\sqrt{7}\). In exams, simplify \(\sqrt{28}=2\sqrt{7}\).
Step 2
Why this answer is correct
The correct answer is A. \(x=-6\pm2\sqrt{7}\). Since ((x+6)2 =28), \(x=-6\pm2\sqrt{7}\). In exams, simplify \(\sqrt{28}=2\sqrt{7}\).
Step 3
Exam Tip
((x+6)2 =28), इसलिए \(x=-6\pm2\sqrt{7}\) है। परीक्षा में \(\sqrt{28}=2\sqrt{7}\) सरल करें।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि \(x^2+12x+8=0\), तो पूर्ण वर्ग विधि से सही रूप कौनसा है?
If \(x^2+12x+8=0\), which form is correct by completing square?
#quadratic
#completing-square
#irrational-roots
A ((x+6)2 =28)
B ((x-6)2 =28)
C ((x+12)2 =8)
D ((x+6)2 =8)
Explanation opens after your attempt
Correct Answer
A. ((x+6)2 =28)
Step 1
Concept
Adding (36) to \(x^2+12x=-8\) gives ((x+6)2 =28). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x+6)2 =28). Adding (36) to \(x^2+12x=-8\) gives ((x+6)2 =28). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2+12x=-8\) में (36) जोड़ने पर ((x+6)2 =28) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(11x^2-44x+7=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?
What roots are obtained for \(11x^2-44x+7=0\) by completing square method?
#quadratic
#completing-square
#irrational-roots
A \(x=2\pm\frac{\sqrt{407}}{11}\)
B \(x=-2\pm\frac{\sqrt{407}}{11}\)
C \(x=4\pm\sqrt{407}\)
D \(x=2\pm\frac{\sqrt{37}}{11}\)
Explanation opens after your attempt
Correct Answer
A. \(x=2\pm\frac{\sqrt{407}}{11}\)
Step 1
Concept
Since ((x-2)2 =\frac{37}{11}), \(x=2\pm\sqrt{\frac{37}{11}}=2\pm\frac{\sqrt{407}}{11}\). In exams, rationalize the denominator.
Step 2
Why this answer is correct
The correct answer is A. \(x=2\pm\frac{\sqrt{407}}{11}\). Since ((x-2)2 =\frac{37}{11}), \(x=2\pm\sqrt{\frac{37}{11}}=2\pm\frac{\sqrt{407}}{11}\). In exams, rationalize the denominator.
Step 3
Exam Tip
((x-2)2 =\frac{37}{11}), इसलिए \(x=2\pm\sqrt{\frac{37}{11}}=2\pm\frac{\sqrt{407}}{11}\) है। परीक्षा में हर को परिमेय बनाएं।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(11x^2-44x+7=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(11x^2-44x+7=0\) by completing the square?
#quadratic
#completing-square
#expert
A ((x-2)2 =\frac{37}{11})
B ((x+2)2 =\frac{37}{11})
C ((x-4)2 =\frac{7}{11})
D ((x-2)2 =4)
Explanation opens after your attempt
Correct Answer
A. ((x-2)2 =\frac{37}{11})
Step 1
Concept
First \(x^2-4x+\frac{7}{11}=0\) is obtained, then ((x-2)2 =\frac{37}{11}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. ((x-2)2 =\frac{37}{11}). First \(x^2-4x+\frac{7}{11}=0\) is obtained, then ((x-2)2 =\frac{37}{11}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2-4x+\frac{7}{11}=0\) बनता है, फिर ((x-2)2 =\frac{37}{11}) मिलता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(5x^2-10x+13=0\) में पूर्ण वर्ग रूप कौनसा सही है?
Which completed square form is correct for \(5x^2-10x+13=0\)?
#quadratic
#completing-square
#no-real-roots
A (5(x-1)2 +8=0)
B (5(x+1)2 +8=0)
C (5(x-1)2 -8=0)
D (5(x-2)2 +13=0)
Explanation opens after your attempt
Correct Answer
A. (5(x-1)2 +8=0)
Step 1
Concept
(5x-2 -10x+13=5(x-1)2 +8), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. (5(x-1)2 +8=0). (5x-2 -10x+13=5(x-1)2 +8), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 3
Exam Tip
(5x-2 -10x+13=5(x-1)2 +8), इसलिए यह वास्तविक (x) के लिए शून्य नहीं हो सकता। परीक्षा में पूर्ण वर्ग रूप से भी मूलों की प्रकृति दिखती है।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(x^2+10x+6=0\) के मूल क्या हैं?
What are the roots of \(x^2+10x+6=0\)?
#quadratic
#completing-square
#roots
A \(x=-5\pm\sqrt{19}\)
B \(x=5\pm\sqrt{19}\)
C \(x=-10\pm\sqrt{19}\)
D \(x=-5\pm19\)
Explanation opens after your attempt
Correct Answer
A. \(x=-5\pm\sqrt{19}\)
Step 1
Concept
Since ((x+5)2 =19), \(x=-5\pm\sqrt{19}\). In exams, write both values using \(\pm\).
Step 2
Why this answer is correct
The correct answer is A. \(x=-5\pm\sqrt{19}\). Since ((x+5)2 =19), \(x=-5\pm\sqrt{19}\). In exams, write both values using \(\pm\).
Step 3
Exam Tip
((x+5)2 =19), इसलिए \(x=-5\pm\sqrt{19}\) है। परीक्षा में \(\pm\) के दोनों मान लिखें।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि \(x^2+10x+6=0\), तो पूर्ण वर्ग विधि से सही रूप कौनसा है?
If \(x^2+10x+6=0\), which form is correct by completing square?
#quadratic
#completing-square
#irrational-roots
A ((x+5)2 =19)
B ((x-5)2 =19)
C ((x+10)2 =6)
D ((x+5)2 =6)
Explanation opens after your attempt
Correct Answer
A. ((x+5)2 =19)
Step 1
Concept
Adding (25) to \(x^2+10x=-6\) gives ((x+5)2 =19). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x+5)2 =19). Adding (25) to \(x^2+10x=-6\) gives ((x+5)2 =19). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2+10x=-6\) में (25) जोड़ने पर ((x+5)2 =19) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(9x^2-30x+8=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?
What roots are obtained for \(9x^2-30x+8=0\) by completing square method?
#quadratic
#completing-square
#irrational-roots
A \(x=\frac{5\pm\sqrt{17}}{3}\)
B \(x=\frac{-5\pm\sqrt{17}}{3}\)
C \(x=5\pm\sqrt{17}\)
D \(x=\frac{10\pm\sqrt{17}}{9}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{5\pm\sqrt{17}}{3}\)
Step 1
Concept
Since (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9}), \(x=\frac{5\pm\sqrt{17}}{3}\). In exams, write the square root with the denominator correctly.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{5\pm\sqrt{17}}{3}\). Since (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9}), \(x=\frac{5\pm\sqrt{17}}{3}\). In exams, write the square root with the denominator correctly.
Step 3
Exam Tip
(\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9}), इसलिए \(x=\frac{5\pm\sqrt{17}}{3}\) है। परीक्षा में वर्गमूल को हर के साथ सही लिखें।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(9x^2-30x+8=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(9x^2-30x+8=0\) by completing the square?
#quadratic
#completing-square
#expert
A (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9})
B (\left\(x+\frac{5}{3}\right\)2 =\frac{17}{9})
C (\left\(x-\frac{10}{3}\right\)2 =\frac{8}{9})
D (\left\(x-\frac{5}{3}\right\)2 =\frac{25}{9})
Explanation opens after your attempt
Correct Answer
A. (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9})
Step 1
Concept
First \(x^2-\frac{10}{3}x+\frac{8}{9}=0\) is obtained, then (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9}). First \(x^2-\frac{10}{3}x+\frac{8}{9}=0\) is obtained, then (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2-\frac{10}{3}x+\frac{8}{9}=0\) बनता है, फिर (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9}) मिलता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(4x^2-8x+9=0\) में पूर्ण वर्ग रूप कौनसा सही है?
Which completed square form is correct for \(4x^2-8x+9=0\)?
#quadratic
#completing-square
#no-real-roots
A (4(x-1)2 +5=0)
B (4(x+1)2 +5=0)
C (4(x-1)2 -5=0)
D (4(x-2)2 +9=0)
Explanation opens after your attempt
Correct Answer
A. (4(x-1)2 +5=0)
Step 1
Concept
(4x-2 -8x+9=4(x-1)2 +5), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. (4(x-1)2 +5=0). (4x-2 -8x+9=4(x-1)2 +5), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 3
Exam Tip
(4x-2 -8x+9=4(x-1)2 +5), इसलिए यह वास्तविक (x) के लिए शून्य नहीं हो सकता। परीक्षा में पूर्ण वर्ग रूप से भी मूलों की प्रकृति दिखती है।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(x^2+8x+5=0\) के मूल क्या हैं?
What are the roots of \(x^2+8x+5=0\)?
#quadratic
#completing-square
#roots
A \(x=-4\pm\sqrt{11}\)
B \(x=4\pm\sqrt{11}\)
C \(x=-8\pm\sqrt{11}\)
D \(x=-4\pm11\)
Explanation opens after your attempt
Correct Answer
A. \(x=-4\pm\sqrt{11}\)
Step 1
Concept
Since ((x+4)2 =11), \(x=-4\pm\sqrt{11}\). In exams, write both values using \(\pm\).
Step 2
Why this answer is correct
The correct answer is A. \(x=-4\pm\sqrt{11}\). Since ((x+4)2 =11), \(x=-4\pm\sqrt{11}\). In exams, write both values using \(\pm\).
Step 3
Exam Tip
((x+4)2 =11), इसलिए \(x=-4\pm\sqrt{11}\) है। परीक्षा में \(\pm\) के दोनों मान लिखें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि \(x^2+8x+5=0\), तो पूर्ण वर्ग विधि से सही रूप कौनसा है?
If \(x^2+8x+5=0\), which form is correct by completing square?
#quadratic
#completing-square
#irrational-roots
A ((x+4)2 =11)
B ((x-4)2 =11)
C ((x+8)2 =5)
D ((x+4)2 =5)
Explanation opens after your attempt
Correct Answer
A. ((x+4)2 =11)
Step 1
Concept
Adding (16) to \(x^2+8x=-5\) gives ((x+4)2 =11). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x+4)2 =11). Adding (16) to \(x^2+8x=-5\) gives ((x+4)2 =11). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2+8x=-5\) में (16) जोड़ने पर ((x+4)2 =11) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(7x^2-22x+7=0\) के मूल क्या होंगे?
What will be the roots of \(7x^2-22x+7=0\)?
#quadratic
#completing-square
#irrational-roots
A \(x=\frac{11\pm6\sqrt{2}}{7}\)
B \(x=\frac{-11\pm6\sqrt{2}}{7}\)
C \(x=\frac{22\pm6\sqrt{2}}{7}\)
D \(x=\frac{11\pm\sqrt{2}}{7}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{11\pm6\sqrt{2}}{7}\)
Step 1
Concept
Since (\left\(x-\frac{11}{7}\right\)2 =\frac{72}{49}), \(x=\frac{11\pm6\sqrt{2}}{7}\). In exams, simplify \(\sqrt{72}=6\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{11\pm6\sqrt{2}}{7}\). Since (\left\(x-\frac{11}{7}\right\)2 =\frac{72}{49}), \(x=\frac{11\pm6\sqrt{2}}{7}\). In exams, simplify \(\sqrt{72}=6\sqrt{2}\).
Step 3
Exam Tip
(\left\(x-\frac{11}{7}\right\)2 =\frac{72}{49}), इसलिए \(x=\frac{11\pm6\sqrt{2}}{7}\) है। परीक्षा में \(\sqrt{72}=6\sqrt{2}\) सरल करें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(7x^2-22x+7=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(7x^2-22x+7=0\) by completing the square?
#quadratic
#completing-square
#hard
A (\left\(x-\frac{11}{7}\right\)2 =\frac{72}{49})
B (\left\(x+\frac{11}{7}\right\)2 =\frac{72}{49})
C (\left\(x-\frac{22}{7}\right\)2 =1)
D (\left\(x-\frac{11}{7}\right\)2 =\frac{121}{49})
Explanation opens after your attempt
Correct Answer
A. (\left\(x-\frac{11}{7}\right\)2 =\frac{72}{49})
Step 1
Concept
First \(x^2-\frac{22}{7}x+1=0\) is obtained, then (\left\(x-\frac{11}{7}\right\)2 =\frac{72}{49}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. (\left\(x-\frac{11}{7}\right\)2 =\frac{72}{49}). First \(x^2-\frac{22}{7}x+1=0\) is obtained, then (\left\(x-\frac{11}{7}\right\)2 =\frac{72}{49}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2-\frac{22}{7}x+1=0\) बनता है, फिर (\left\(x-\frac{11}{7}\right\)2 =\frac{72}{49}) मिलता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि \(2x^2+10x+3=0\) को पूर्ण वर्ग विधि से हल किया जाए, तो सही मध्य चरण कौनसा है?
If \(2x^2+10x+3=0\) is solved by completing the square, which middle step is correct?
#quadratic
#completing-square
#hard
A (\left\(x+\frac{5}{2}\right\)2 =\frac{19}{4})
B (\left\(x-\frac{5}{2}\right\)2 =\frac{19}{4})
C ((x+5)2 =\frac{3}{2})
D (\left\(x+\frac{5}{2}\right\)2 =\frac{25}{4})
Explanation opens after your attempt
Correct Answer
A. (\left\(x+\frac{5}{2}\right\)2 =\frac{19}{4})
Step 1
Concept
First \(x^2+5x+\frac{3}{2}=0\) is obtained, then adding \(\frac{25}{4}\) gives (\left\(x+\frac{5}{2}\right\)2 =\frac{19}{4}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. (\left\(x+\frac{5}{2}\right\)2 =\frac{19}{4}). First \(x^2+5x+\frac{3}{2}=0\) is obtained, then adding \(\frac{25}{4}\) gives (\left\(x+\frac{5}{2}\right\)2 =\frac{19}{4}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2+5x+\frac{3}{2}=0\) मिलता है, फिर \(\frac{25}{4}\) जोड़ने पर (\left\(x+\frac{5}{2}\right\)2 =\frac{19}{4}) बनता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(3x^2-6x+7=0\) में पूर्ण वर्ग रूप कौनसा सही है?
Which completed square form is correct for \(3x^2-6x+7=0\)?
#quadratic
#completing-square
#no-real-roots
A (3(x-1)2 +4=0)
B (3(x+1)2 +4=0)
C (3(x-1)2 -4=0)
D (3(x-2)2 +7=0)
Explanation opens after your attempt
Correct Answer
A. (3(x-1)2 +4=0)
Step 1
Concept
(3x-2 -6x+7=3(x-1)2 +4), so it cannot be zero for real (x). In exams, completed square form also shows the nature of real roots.
Step 2
Why this answer is correct
The correct answer is A. (3(x-1)2 +4=0). (3x-2 -6x+7=3(x-1)2 +4), so it cannot be zero for real (x). In exams, completed square form also shows the nature of real roots.
Step 3
Exam Tip
(3x-2 -6x+7=3(x-1)2 +4), इसलिए यह वास्तविक (x) के लिए शून्य नहीं हो सकता। परीक्षा में पूर्ण वर्ग रूप से भी वास्तविक मूलों की प्रकृति दिखती है।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(x^2+6x+2=0\) के मूल क्या हैं?
What are the roots of \(x^2+6x+2=0\)?
#quadratic
#completing-square
#roots
A \(x=-3\pm\sqrt{7}\)
B \(x=3\pm\sqrt{7}\)
C \(x=-6\pm\sqrt{7}\)
D \(x=-3\pm7\)
Explanation opens after your attempt
Correct Answer
A. \(x=-3\pm\sqrt{7}\)
Step 1
Concept
Since ((x+3)2 =7), \(x=-3\pm\sqrt{7}\). In exams, write both values using \(\pm\).
Step 2
Why this answer is correct
The correct answer is A. \(x=-3\pm\sqrt{7}\). Since ((x+3)2 =7), \(x=-3\pm\sqrt{7}\). In exams, write both values using \(\pm\).
Step 3
Exam Tip
((x+3)2 =7), इसलिए \(x=-3\pm\sqrt{7}\) है। परीक्षा में \(\pm\) के दोनों मान लिखें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि \(x^2+6x+2=0\), तो पूर्ण वर्ग विधि से सही रूप कौनसा है?
If \(x^2+6x+2=0\), which form is correct by completing square?
#quadratic
#completing-square
#irrational-roots
A ((x+3)2 =7)
B ((x-3)2 =7)
C ((x+6)2 =2)
D ((x+3)2 =2)
Explanation opens after your attempt
Correct Answer
A. ((x+3)2 =7)
Step 1
Concept
Adding (9) to \(x^2+6x=-2\) gives ((x+3)2 =7). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x+3)2 =7). Adding (9) to \(x^2+6x=-2\) gives ((x+3)2 =7). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2+6x=-2\) में (9) जोड़ने पर ((x+3)2 =7) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(5x^2-18x+9=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(5x^2-18x+9=0\) by completing the square?
#quadratic
#completing-square
#hard
A (\left\(x-\frac{9}{5}\right\)2 =\frac{36}{25})
B (\left\(x+\frac{9}{5}\right\)2 =\frac{36}{25})
C (\left\(x-\frac{18}{5}\right\)2 =\frac{9}{5})
D (\left\(x-\frac{9}{5}\right\)2 =\frac{81}{25})
Explanation opens after your attempt
Correct Answer
A. (\left\(x-\frac{9}{5}\right\)2 =\frac{36}{25})
Step 1
Concept
First \(x^2-\frac{18}{5}x+\frac{9}{5}=0\) is obtained, then (\left\(x-\frac{9}{5}\right\)2 =\frac{36}{25}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. (\left\(x-\frac{9}{5}\right\)2 =\frac{36}{25}). First \(x^2-\frac{18}{5}x+\frac{9}{5}=0\) is obtained, then (\left\(x-\frac{9}{5}\right\)2 =\frac{36}{25}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2-\frac{18}{5}x+\frac{9}{5}=0\) बनता है, फिर (\left\(x-\frac{9}{5}\right\)2 =\frac{36}{25}) मिलता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(2x^2+8x+1=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?
What roots are obtained for \(2x^2+8x+1=0\) by completing the square method?
#quadratic
#completing-square
#irrational-roots
A \(x=-2\pm\frac{\sqrt{14}}{2}\)
B \(x=2\pm\frac{\sqrt{14}}{2}\)
C \(x=-4\pm\sqrt{14}\)
D \(x=-2\pm\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(x=-2\pm\frac{\sqrt{14}}{2}\)
Step 1
Concept
Since ((x+2)2 =\frac{7}{2}), \(x=-2\pm\sqrt{\frac{7}{2}}=-2\pm\frac{\sqrt{14}}{2}\). In exams, write the square root in simplified form.
Step 2
Why this answer is correct
The correct answer is A. \(x=-2\pm\frac{\sqrt{14}}{2}\). Since ((x+2)2 =\frac{7}{2}), \(x=-2\pm\sqrt{\frac{7}{2}}=-2\pm\frac{\sqrt{14}}{2}\). In exams, write the square root in simplified form.
Step 3
Exam Tip
((x+2)2 =\frac{7}{2}), इसलिए \(x=-2\pm\sqrt{\frac{7}{2}}=-2\pm\frac{\sqrt{14}}{2}\) है। परीक्षा में वर्गमूल को सरल रूप में लिखें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि \(2x^2+8x+1=0\) को पूर्ण वर्ग विधि से हल किया जाए, तो सही मध्य चरण कौनसा है?
If \(2x^2+8x+1=0\) is solved by completing the square, which middle step is correct?
#quadratic
#completing-square
#hard
A ((x+2)2 =\frac{7}{2})
B ((x-2)2 =\frac{7}{2})
C ((x+4)2 =\frac{1}{2})
D ((x+2)2 =7)
Explanation opens after your attempt
Correct Answer
A. ((x+2)2 =\frac{7}{2})
Step 1
Concept
First \(x^2+4x+\frac{1}{2}=0\) is obtained, then adding (4) gives ((x+2)2 =\frac{7}{2}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. ((x+2)2 =\frac{7}{2}). First \(x^2+4x+\frac{1}{2}=0\) is obtained, then adding (4) gives ((x+2)2 =\frac{7}{2}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2+4x+\frac{1}{2}=0\) मिलता है, फिर (4) जोड़ने पर ((x+2)2 =\frac{7}{2}) बनता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(2x^2-4x+5=0\) में पूर्ण वर्ग रूप कौनसा सही है?
Which completed square form is correct for \(2x^2-4x+5=0\)?
#quadratic
#completing-square
#no-real-roots
A (2(x-1)2 +3=0)
B (2(x+1)2 +3=0)
C (2(x-1)2 -3=0)
D (2(x-2)2 +5=0)
Explanation opens after your attempt
Correct Answer
A. (2(x-1)2 +3=0)
Step 1
Concept
(2x-2 -4x+5=2(x-1)2 +3), so it cannot be zero for real (x). In exams, completed square form also shows no real roots.
Step 2
Why this answer is correct
The correct answer is A. (2(x-1)2 +3=0). (2x-2 -4x+5=2(x-1)2 +3), so it cannot be zero for real (x). In exams, completed square form also shows no real roots.
Step 3
Exam Tip
(2x-2 -4x+5=2(x-1)2 +3), इसलिए यह वास्तविक (x) के लिए शून्य नहीं हो सकता। परीक्षा में पूर्ण वर्ग रूप से भी no real roots दिखता है।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(x^2+4x+1=0\) के मूल क्या हैं?
What are the roots of \(x^2+4x+1=0\)?
#quadratic
#completing-square
#roots
A \(x=-2\pm\sqrt{3}\)
B \(x=2\pm\sqrt{3}\)
C \(x=-4\pm\sqrt{3}\)
D \(x=-2\pm3\)
Explanation opens after your attempt
Correct Answer
A. \(x=-2\pm\sqrt{3}\)
Step 1
Concept
Since ((x+2)2 =3), \(x=-2\pm\sqrt{3}\). In exams, write both values using \(\pm\).
Step 2
Why this answer is correct
The correct answer is A. \(x=-2\pm\sqrt{3}\). Since ((x+2)2 =3), \(x=-2\pm\sqrt{3}\). In exams, write both values using \(\pm\).
Step 3
Exam Tip
((x+2)2 =3), इसलिए \(x=-2\pm\sqrt{3}\) है। परीक्षा में \(\pm\) के दोनों मान लिखें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि \(x^2+4x+1=0\), तो पूर्ण वर्ग विधि से सही रूप कौनसा है?
If \(x^2+4x+1=0\), which form is correct by completing square?
#quadratic
#completing-square
#irrational-roots
A ((x+2)2 =3)
B ((x-2)2 =3)
C ((x+4)2 =1)
D ((x+2)2 =1)
Explanation opens after your attempt
Correct Answer
A. ((x+2)2 =3)
Step 1
Concept
Adding (4) to \(x^2+4x=-1\) gives ((x+2)2 =3). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x+2)2 =3). Adding (4) to \(x^2+4x=-1\) gives ((x+2)2 =3). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2+4x=-1\) में (4) जोड़ने पर ((x+2)2 =3) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(3x^2-10x+3=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(3x^2-10x+3=0\) by completing the square?
#quadratic
#completing-square
#hard
A (\left\(x-\frac{5}{3}\right\)2 =\frac{16}{9})
B (\left\(x+\frac{5}{3}\right\)2 =\frac{16}{9})
C (\left\(x-\frac{10}{3}\right\)2 =1)
D (\left\(x-\frac{5}{3}\right\)2 =\frac{25}{9})
Explanation opens after your attempt
Correct Answer
A. (\left\(x-\frac{5}{3}\right\)2 =\frac{16}{9})
Step 1
Concept
First we get \(x^2-\frac{10}{3}x+1=0\), then (\left\(x-\frac{5}{3}\right\)2 =\frac{16}{9}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. (\left\(x-\frac{5}{3}\right\)2 =\frac{16}{9}). First we get \(x^2-\frac{10}{3}x+1=0\), then (\left\(x-\frac{5}{3}\right\)2 =\frac{16}{9}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2-\frac{10}{3}x+1=0\) बनता है और फिर (\left\(x-\frac{5}{3}\right\)2 =\frac{16}{9}) मिलता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(x^2-24x+108=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?
What roots are obtained for \(x^2-24x+108=0\) by completing the square method?
#quadratic
#completing-square
#roots
A (x=6,18)
B (x=-6,-18)
C (x=12,6)
D (x=24,108)
Explanation opens after your attempt
Correct Answer
A. (x=6,18)
Step 1
Concept
Since ((x-12)2 =36), \(x-12=\pm6\), so (x=6,18). In exams, use \(\pm\) to find both roots.
Step 2
Why this answer is correct
The correct answer is A. (x=6,18). Since ((x-12)2 =36), \(x-12=\pm6\), so (x=6,18). In exams, use \(\pm\) to find both roots.
Step 3
Exam Tip
((x-12)2 =36), इसलिए \(x-12=\pm6\) और (x=6,18) हैं। परीक्षा में \(\pm\) से दोनों मूल निकालें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि \(x^2-24x+108=0\) को पूर्ण वर्ग विधि से हल किया जाए, तो सही मध्य चरण कौनसा है?
If \(x^2-24x+108=0\) is solved by completing the square, which middle step is correct?
#quadratic
#completing-square
#steps
A ((x-12)2 =36)
B ((x+12)2 =36)
C ((x-24)2 =108)
D ((x-12)2 =108)
Explanation opens after your attempt
Correct Answer
A. ((x-12)2 =36)
Step 1
Concept
Adding (144) to \(x^2-24x=-108\) gives ((x-12)2 =36). In exams, add the square of half the coefficient to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x-12)2 =36). Adding (144) to \(x^2-24x=-108\) gives ((x-12)2 =36). In exams, add the square of half the coefficient to both sides.
Step 3
Exam Tip
\(x^2-24x=-108\) में (144) जोड़ने पर ((x-12)2 =36) मिलता है। परीक्षा में आधे गुणांक का वर्ग दोनों पक्षों में जोड़ें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(x^2-6x+18=0\) में पूर्ण वर्ग बनाने पर कौनसा रूप बनेगा?
What form is obtained by completing the square in \(x^2-6x+18=0\)?
#quadratic
#completing-square
#no-real-roots
A ((x-3)2 +9=0)
B ((x+3)2 +9=0)
C ((x-3)2 -9=0)
D ((x+6)2 +3=0)
Explanation opens after your attempt
Correct Answer
A. ((x-3)2 +9=0)
Step 1
Concept
(x-2 -6x+18=(x-3)2 +9), so no real roots are obtained. In exams, use completed square form to understand the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. ((x-3)2 +9=0). (x-2 -6x+18=(x-3)2 +9), so no real roots are obtained. In exams, use completed square form to understand the nature of roots.
Step 3
Exam Tip
(x-2 -6x+18=(x-3)2 +9), इसलिए वास्तविक मूल नहीं मिलते। परीक्षा में पूर्ण वर्ग रूप से भी मूलों की प्रकृति समझें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(x^2+8x-33=0\) के मूल क्या हैं?
What are the roots of \(x^2+8x-33=0\)?
#quadratic
#completing-square
#roots
A (x=3,-11)
B (x=-3,11)
C (x=7,-7)
D (x=8,-33)
Explanation opens after your attempt
Correct Answer
A. (x=3,-11)
Step 1
Concept
Since ((x+4)2 =49), \(x+4=\pm7\), so (x=3,-11). In exams, use \(\pm\) to get both answers.
Step 2
Why this answer is correct
The correct answer is A. (x=3,-11). Since ((x+4)2 =49), \(x+4=\pm7\), so (x=3,-11). In exams, use \(\pm\) to get both answers.
Step 3
Exam Tip
((x+4)2 =49), इसलिए \(x+4=\pm7\) और (x=3,-11) हैं। परीक्षा में \(\pm\) से दोनों उत्तर निकालें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(x^2+8x-33=0\) को पूर्ण वर्ग विधि से हल करने में सही चरण कौनसा है?
Which step is correct in solving \(x^2+8x-33=0\) by completing square?
#quadratic
#completing-square
#steps
A ((x+4)2 =49)
B ((x-4)2 =49)
C ((x+8)2 =33)
D ((x+4)2 =33)
Explanation opens after your attempt
Correct Answer
A. ((x+4)2 =49)
Step 1
Concept
Adding (16) to \(x^2+8x=33\) gives ((x+4)2 =49). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. ((x+4)2 =49). Adding (16) to \(x^2+8x=33\) gives ((x+4)2 =49). In exams, add the square of half the coefficient.
Step 3
Exam Tip
\(x^2+8x=33\) में (16) जोड़ने पर ((x+4)2 =49) मिलता है। परीक्षा में आधे गुणांक का वर्ग जोड़ें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(x^2-18x+45=0\) के मूल क्या हैं?
What are the roots of \(x^2-18x+45=0\)?
#quadratic
#completing-square
#roots
A (x=3,15)
B (x=-3,-15)
C (x=6,12)
D (x=9,36)
Explanation opens after your attempt
Correct Answer
A. (x=3,15)
Step 1
Concept
Since ((x-9)2 =36), \(x-9=\pm6\), so (x=3,15). In exams, use \(\pm\) to find both roots.
Step 2
Why this answer is correct
The correct answer is A. (x=3,15). Since ((x-9)2 =36), \(x-9=\pm6\), so (x=3,15). In exams, use \(\pm\) to find both roots.
Step 3
Exam Tip
((x-9)2 =36), इसलिए \(x-9=\pm6\) और (x=3,15) हैं। परीक्षा में \(\pm\) से दोनों मूल निकालें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(x^2-18x+45=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(x^2-18x+45=0\) by completing square?
#quadratic
#completing-square
#steps
A ((x-9)2 =36)
B ((x+9)2 =36)
C ((x-18)2 =45)
D ((x-9)2 =45)
Explanation opens after your attempt
Correct Answer
A. ((x-9)2 =36)
Step 1
Concept
Adding (81) to \(x^2-18x=-45\) gives ((x-9)2 =36). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. ((x-9)2 =36). Adding (81) to \(x^2-18x=-45\) gives ((x-9)2 =36). In exams, add the square of half the coefficient.
Step 3
Exam Tip
\(x^2-18x=-45\) में (81) जोड़ने पर ((x-9)2 =36) मिलता है। परीक्षा में आधे गुणांक का वर्ग जोड़ें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(x^2-10x+24=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(x^2-10x+24=0\) by completing the square?
#quadratic
#completing-square
#steps
A ((x-5)2 =1)
B ((x+5)2 =1)
C ((x-10)2 =24)
D ((x-5)2 =24)
Explanation opens after your attempt
Correct Answer
A. ((x-5)2 =1)
Step 1
Concept
Adding (25) to \(x^2-10x=-24\) gives ((x-5)2 =1). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x-5)2 =1). Adding (25) to \(x^2-10x=-24\) gives ((x-5)2 =1). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2-10x=-24\) में (25) जोड़ने पर ((x-5)2 =1) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(x^2-6x-7=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?
What roots are obtained for \(x^2-6x-7=0\) by completing the square method?
#quadratic
#completing-square
#roots
A (x=7,-1)
B (x=-7,1)
C (x=3,4)
D (x=6,-7)
Explanation opens after your attempt
Correct Answer
A. (x=7,-1)
Step 1
Concept
Since ((x-3)2 =16), \(x-3=\pm4\), so (x=7,-1). In exams, use \(\pm\) to find both roots.
Step 2
Why this answer is correct
The correct answer is A. (x=7,-1). Since ((x-3)2 =16), \(x-3=\pm4\), so (x=7,-1). In exams, use \(\pm\) to find both roots.
Step 3
Exam Tip
((x-3)2 =16), इसलिए \(x-3=\pm4\) और (x=7,-1) हैं। परीक्षा में \(\pm\) से दोनों मूल निकालें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि \(x^2-6x-7=0\) को पूर्ण वर्ग विधि से हल किया जाए, तो सही मध्य चरण कौनसा है?
If \(x^2-6x-7=0\) is solved by completing the square, which middle step is correct?
#quadratic
#completing-square
#steps
A ((x-3)2 =16)
B ((x+3)2 =16)
C ((x-6)2 =7)
D ((x-3)2 =7)
Explanation opens after your attempt
Correct Answer
A. ((x-3)2 =16)
Step 1
Concept
Adding (9) to \(x^2-6x=7\) gives ((x-3)2 =16). In exams, add the square of half the coefficient to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x-3)2 =16). Adding (9) to \(x^2-6x=7\) gives ((x-3)2 =16). In exams, add the square of half the coefficient to both sides.
Step 3
Exam Tip
\(x^2-6x=7\) में (9) जोड़ने पर ((x-3)2 =16) मिलता है। परीक्षा में आधे गुणांक का वर्ग दोनों पक्षों में जोड़ें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(x^2-4x+13=0\) में पूर्ण वर्ग बनाने पर कौनसा रूप बनेगा?
What form is obtained by completing the square in \(x^2-4x+13=0\)?
#quadratic
#completing-square
#no-real-roots
A ((x-2)2 +9=0)
B ((x+2)2 +9=0)
C ((x-2)2 -9=0)
D ((x+4)2 +2=0)
Explanation opens after your attempt
Correct Answer
A. ((x-2)2 +9=0)
Step 1
Concept
(x-2 -4x+13=(x-2)2 +9), so no real roots are obtained. In exams, use completed square form to understand the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. ((x-2)2 +9=0). (x-2 -4x+13=(x-2)2 +9), so no real roots are obtained. In exams, use completed square form to understand the nature of roots.
Step 3
Exam Tip
(x-2 -4x+13=(x-2)2 +9), इसलिए वास्तविक मूल नहीं मिलते। परीक्षा में पूर्ण वर्ग रूप से भी मूलों की प्रकृति समझें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(x^2+2x-24=0\) के मूल क्या हैं?
What are the roots of \(x^2+2x-24=0\)?
#quadratic
#completing-square
#roots
A (x=4,-6)
B (x=-4,6)
C (x=5,-5)
D (x=2,-12)
Explanation opens after your attempt
Correct Answer
A. (x=4,-6)
Step 1
Concept
Since ((x+1)2 =25), \(x+1=\pm5\), so (x=4,-6). In exams, use \(\pm\) to get both answers.
Step 2
Why this answer is correct
The correct answer is A. (x=4,-6). Since ((x+1)2 =25), \(x+1=\pm5\), so (x=4,-6). In exams, use \(\pm\) to get both answers.
Step 3
Exam Tip
((x+1)2 =25), इसलिए \(x+1=\pm5\) और (x=4,-6) हैं। परीक्षा में \(\pm\) से दोनों उत्तर निकालें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(x^2+2x-24=0\) को पूर्ण वर्ग विधि से हल करने में सही चरण कौनसा है?
Which step is correct in solving \(x^2+2x-24=0\) by completing square?
#quadratic
#completing-square
#steps
A ((x+1)2 =25)
B ((x-1)2 =25)
C ((x+2)2 =24)
D ((x+1)2 =24)
Explanation opens after your attempt
Correct Answer
A. ((x+1)2 =25)
Step 1
Concept
Adding (1) to \(x^2+2x=24\) gives ((x+1)2 =25). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. ((x+1)2 =25). Adding (1) to \(x^2+2x=24\) gives ((x+1)2 =25). In exams, add the square of half the coefficient.
Step 3
Exam Tip
\(x^2+2x=24\) में (1) जोड़ने पर ((x+1)2 =25) मिलता है। परीक्षा में आधे गुणांक का वर्ग जोड़ें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(x^2-16x+28=0\) के मूल क्या हैं?
What are the roots of \(x^2-16x+28=0\)?
#quadratic
#completing-square
#roots
A (x=2,14)
B (x=-2,-14)
C (x=4,12)
D (x=8,6)
Explanation opens after your attempt
Correct Answer
A. (x=2,14)
Step 1
Concept
Since ((x-8)2 =36), \(x-8=\pm6\), so (x=2,14). In exams, use \(\pm\) to find both roots.
Step 2
Why this answer is correct
The correct answer is A. (x=2,14). Since ((x-8)2 =36), \(x-8=\pm6\), so (x=2,14). In exams, use \(\pm\) to find both roots.
Step 3
Exam Tip
((x-8)2 =36), इसलिए \(x-8=\pm6\) और (x=2,14) हैं। परीक्षा में \(\pm\) से दोनों मूल निकालें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(x^2-16x+28=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(x^2-16x+28=0\) by completing square?
#quadratic
#completing-square
#steps
A ((x-8)2 =36)
B ((x+8)2 =36)
C ((x-16)2 =28)
D ((x-8)2 =28)
Explanation opens after your attempt
Correct Answer
A. ((x-8)2 =36)
Step 1
Concept
Adding (64) to \(x^2-16x=-28\) gives ((x-8)2 =36). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. ((x-8)2 =36). Adding (64) to \(x^2-16x=-28\) gives ((x-8)2 =36). In exams, add the square of half the coefficient.
Step 3
Exam Tip
\(x^2-16x=-28\) में (64) जोड़ने पर ((x-8)2 =36) मिलता है। परीक्षा में आधे गुणांक का वर्ग जोड़ें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(x^2-8x+12=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(x^2-8x+12=0\) by completing the square?
#quadratic
#completing-square
#steps
A ((x-4)2 =4)
B ((x+4)2 =4)
C ((x-8)2 =12)
D ((x-4)2 =12)
Explanation opens after your attempt
Correct Answer
A. ((x-4)2 =4)
Step 1
Concept
Adding (16) to \(x^2-8x=-12\) gives ((x-4)2 =4). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x-4)2 =4). Adding (16) to \(x^2-8x=-12\) gives ((x-4)2 =4). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2-8x=-12\) में (16) जोड़ने पर ((x-4)2 =4) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(x^2-8x+15=0\) के मूल पूर्ण वर्ग विधि से क्या मिलेंगे?
What roots are obtained for \(x^2-8x+15=0\) by completing the square method?
#quadratic
#completing-square
#roots
A (x=3,5)
B (x=-3,-5)
C (x=1,7)
D (x=4,1)
Explanation opens after your attempt
Correct Answer
A. (x=3,5)
Step 1
Concept
Since ((x-4)2 =1), \(x-4=\pm1\), so (x=3,5). In exams, use \(\pm\) to find both roots.
Step 2
Why this answer is correct
The correct answer is A. (x=3,5). Since ((x-4)2 =1), \(x-4=\pm1\), so (x=3,5). In exams, use \(\pm\) to find both roots.
Step 3
Exam Tip
((x-4)2 =1), इसलिए \(x-4=\pm1\) और (x=3,5) हैं। परीक्षा में \(\pm\) से दोनों मूल निकालें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि \(x^2-8x+15=0\) को पूर्ण वर्ग विधि से हल किया जाए, तो सही मध्य चरण कौनसा है?
If \(x^2-8x+15=0\) is solved by completing the square, which middle step is correct?
#quadratic
#completing-square
#steps
A ((x-4)2 =1)
B ((x+4)2 =1)
C ((x-8)2 =15)
D ((x-4)2 =15)
Explanation opens after your attempt
Correct Answer
A. ((x-4)2 =1)
Step 1
Concept
Adding (16) to \(x^2-8x=-15\) gives ((x-4)2 =1). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x-4)2 =1). Adding (16) to \(x^2-8x=-15\) gives ((x-4)2 =1). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2-8x=-15\) में (16) जोड़ने पर ((x-4)2 =1) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(x^2-2x+5=0\) में पूर्ण वर्ग बनाने पर कौनसा रूप बनेगा?
What form is obtained by completing the square in \(x^2-2x+5=0\)?
#quadratic
#completing-square
#no-real-roots
A ((x-1)2 +4=0)
B ((x+1)2 +4=0)
C ((x-1)2 -4=0)
D ((x+2)2 +1=0)
Explanation opens after your attempt
Correct Answer
A. ((x-1)2 +4=0)
Step 1
Concept
(x-2 -2x+5=(x-1)2 +4), so no real roots are obtained. In exams, the completed square form also shows the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. ((x-1)2 +4=0). (x-2 -2x+5=(x-1)2 +4), so no real roots are obtained. In exams, the completed square form also shows the nature of roots.
Step 3
Exam Tip
(x-2 -2x+5=(x-1)2 +4), इसलिए वास्तविक मूल नहीं मिलते। परीक्षा में पूर्ण वर्ग रूप से भी मूलों की प्रकृति समझ सकते हैं।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(x^2+4x-12=0\) के मूल क्या हैं?
What are the roots of \(x^2+4x-12=0\)?
#quadratic
#completing-square
#roots
A (x=2,-6)
B (x=-2,6)
C (x=4,-3)
D (x=-4,3)
Explanation opens after your attempt
Correct Answer
A. (x=2,-6)
Step 1
Concept
Since ((x+2)2 =16), \(x+2=\pm4\), so (x=2,-6). In exams, use \(\pm\) to get both answers.
Step 2
Why this answer is correct
The correct answer is A. (x=2,-6). Since ((x+2)2 =16), \(x+2=\pm4\), so (x=2,-6). In exams, use \(\pm\) to get both answers.
Step 3
Exam Tip
((x+2)2 =16), इसलिए \(x+2=\pm4\) और (x=2,-6) हैं। परीक्षा में \(\pm\) से दोनों उत्तर निकालें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(x^2+4x-12=0\) को पूर्ण वर्ग विधि से हल करने में सही चरण कौनसा है?
Which step is correct in solving \(x^2+4x-12=0\) by completing square?
#quadratic
#completing-square
#steps
A ((x+2)2 =16)
B ((x-2)2 =16)
C ((x+4)2 =12)
D ((x+2)2 =12)
Explanation opens after your attempt
Correct Answer
A. ((x+2)2 =16)
Step 1
Concept
Adding (4) to \(x^2+4x=12\) gives ((x+2)2 =16). In exams, add the same term to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x+2)2 =16). Adding (4) to \(x^2+4x=12\) gives ((x+2)2 =16). In exams, add the same term to both sides.
Step 3
Exam Tip
\(x^2+4x=12\) में (4) जोड़ने पर ((x+2)2 =16) मिलता है। परीक्षा में दोनों पक्षों में समान पद जोड़ें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(x^2-12x+20=0\) के मूल क्या हैं?
What are the roots of \(x^2-12x+20=0\)?
#quadratic
#completing-square
#roots
A (x=2,10)
B (x=-2,-10)
C (x=4,8)
D (x=6,20)
Explanation opens after your attempt
Correct Answer
A. (x=2,10)
Step 1
Concept
Since ((x-6)2 =16), \(x-6=\pm4\), so (x=2,10). In exams, take both values from \(\pm\).
Step 2
Why this answer is correct
The correct answer is A. (x=2,10). Since ((x-6)2 =16), \(x-6=\pm4\), so (x=2,10). In exams, take both values from \(\pm\).
Step 3
Exam Tip
((x-6)2 =16), इसलिए \(x-6=\pm4\) और (x=2,10) हैं। परीक्षा में \(\pm\) के दोनों मान लें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(x^2-12x+20=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(x^2-12x+20=0\) by completing square?
#quadratic
#completing-square
#steps
A ((x-6)2 =16)
B ((x+6)2 =16)
C ((x-12)2 =20)
D ((x-6)2 =36)
Explanation opens after your attempt
Correct Answer
A. ((x-6)2 =16)
Step 1
Concept
From \(x^2-12x+20=0\), \(x^2-12x=-20\), then adding (36) gives ((x-6)2 =16). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x-6)2 =16). From \(x^2-12x+20=0\), \(x^2-12x=-20\), then adding (36) gives ((x-6)2 =16). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2-12x+20=0\) से \(x^2-12x=-20\), फिर (36) जोड़कर ((x-6)2 =16) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(x^2+6x+1=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?
What are the roots of \(x^2+6x+1=0\) by completing the square method?
#quadratic
#completing-square
#irrational-roots
A \(x=-3\pm2\sqrt{2}\)
B \(x=3\pm2\sqrt{2}\)
C \(x=-6\pm\sqrt{2}\)
D \(x=-3\pm\sqrt{8}\)
Explanation opens after your attempt
Correct Answer
A. \(x=-3\pm2\sqrt{2}\)
Step 1
Concept
Since ((x+3)2 =8), \(x=-3\pm2\sqrt{2}\). In exams, simplify \(\sqrt{8}=2\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(x=-3\pm2\sqrt{2}\). Since ((x+3)2 =8), \(x=-3\pm2\sqrt{2}\). In exams, simplify \(\sqrt{8}=2\sqrt{2}\).
Step 3
Exam Tip
((x+3)2 =8), इसलिए \(x=-3\pm2\sqrt{2}\) है। परीक्षा में \(\sqrt{8}=2\sqrt{2}\) सरल करें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(x^2+6x+1=0\) को पूर्ण वर्ग विधि से हल करने पर कौनसा चरण सही है?
Which step is correct while solving \(x^2+6x+1=0\) by completing the square?
#quadratic
#completing-square
#steps
A ((x+3)2 =8)
B ((x+6)2 =35)
C ((x+3)2 =10)
D ((x-3)2 =8)
Explanation opens after your attempt
Correct Answer
A. ((x+3)2 =8)
Step 1
Concept
Adding (9) in \(x^2+6x+1=0\) gives ((x+3)2 =8). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. ((x+3)2 =8). Adding (9) in \(x^2+6x+1=0\) gives ((x+3)2 =8). In exams, add the square of half the coefficient.
Step 3
Exam Tip
\(x^2+6x+1=0\) में (9) जोड़ने पर ((x+3)2 =8) बनता है। परीक्षा में आधे गुणांक का वर्ग जोड़ें।
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Question
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
किस विधि में समीकरण को पहले ((x+p)2 =q) जैसे रूप में बदला जाता है?
In which method is the equation first changed into a form like ((x+p)2 =q)?
#quadratic
#completing-square
#method
A पूर्ण वर्ग विधि / Completing square method
B गुणनखंड विधि / Factorisation method
C वर्गों के अंतर की विधि / Difference of squares method
D शून्य गुणनफल नियम / Zero product rule
Explanation opens after your attempt
Correct Answer
A. पूर्ण वर्ग विधि / Completing square method
Step 1
Concept
In completing square method, the quadratic part is made into the form ((x+p)2 ). In exams, this method is useful when simple factors are not found quickly.
Step 2
Why this answer is correct
The correct answer is A. पूर्ण वर्ग विधि / Completing square method. In completing square method, the quadratic part is made into the form ((x+p)2 ). In exams, this method is useful when simple factors are not found quickly.
Step 3
Exam Tip
पूर्ण वर्ग विधि में द्विघात भाग को ((x+p)2 ) के रूप में बनाया जाता है। परीक्षा में यह विधि तब उपयोगी है जब सामान्य गुणनखंड जल्दी न मिलें।
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Question
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(x^2+24x+144\) किसके बराबर है?
What is \(x^2+24x+144\) equal to?
#quadratic
#perfect-square
#completing-square
A ((x+12)2 )
B ((x-12)2 )
C ((x+24)2 )
D ((x-24)2 )
Explanation opens after your attempt
Correct Answer
A. ((x+12)2 )
Step 1
Concept
(x-2 +24x+144=(x+12)2 ). In exams, identify it using \(2\cdot12x=24x\).
Step 2
Why this answer is correct
The correct answer is A. ((x+12)2 ). (x-2 +24x+144=(x+12)2 ). In exams, identify it using \(2\cdot12x=24x\).
Step 3
Exam Tip
(x-2 +24x+144=(x+12)2 ) है। परीक्षा में \(2\cdot12x=24x\) से पहचान करें।
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Question
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
पूर्ण वर्ग विधि में \(x^2+24x+17=0\) के लिए किस संख्या का प्रयोग होगा?
In completing square method for \(x^2+24x+17=0\), which number will be used?
#quadratic
#completing-square
#number-choice
A (144)
B (24)
C (12)
D (17)
Explanation opens after your attempt
Step 1
Concept
Half of (24) is (12), and \(12^2=144\). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. (144). Half of (24) is (12), and \(12^2=144\). In exams, add the square of half the coefficient.
Step 3
Exam Tip
(24) का आधा (12) है और \(12^2=144\) होता है। परीक्षा में आधे गुणांक का वर्ग जोड़ना होता है।
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Question
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
पूर्ण वर्ग बनाते समय \(x^2-22x\) में कौनसा पद जोड़ना होगा?
While completing the square, which term must be added to \(x^2-22x\)?
#quadratic
#completing-square
#term
A (121)
B (22)
C (11)
D (44)
Explanation opens after your attempt
Step 1
Concept
Half of (-22) is (-11), and ((-11)2 =121). In exams, the square of half the coefficient is always positive.
Step 2
Why this answer is correct
The correct answer is A. (121). Half of (-22) is (-11), and ((-11)2 =121). In exams, the square of half the coefficient is always positive.
Step 3
Exam Tip
(-22) का आधा (-11) है और ((-11)2 =121) होता है। परीक्षा में आधे गुणांक का वर्ग हमेशा धनात्मक होता है।
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Question
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
पूर्ण वर्ग विधि में \(x^2+20x+13=0\) के लिए कौनसी संख्या जोड़ी और घटाई जाएगी?
In completing square method for \(x^2+20x+13=0\), which number will be added and subtracted?
#quadratic
#completing-square
#number-choice
A (100)
B (20)
C (10)
D (13)
Explanation opens after your attempt
Step 1
Concept
Half of (20) is (10), and \(10^2=100\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 2
Why this answer is correct
The correct answer is A. (100). Half of (20) is (10), and \(10^2=100\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 3
Exam Tip
(20) का आधा (10) है और \(10^2=100\) होता है। परीक्षा में (\left\(\frac{b}{2}\right\)2 ) का प्रयोग करें।
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Question
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(x^2+16x+64\) किसके बराबर है?
What is \(x^2+16x+64\) equal to?
#quadratic
#perfect-square
#completing-square
A ((x+8)2 )
B ((x-8)2 )
C ((x+16)2 )
D ((x-16)2 )
Explanation opens after your attempt
Correct Answer
A. ((x+8)2 )
Step 1
Concept
(x-2 +16x+64=(x+8)2 ). In exams, identify it using \(2\cdot8x=16x\).
Step 2
Why this answer is correct
The correct answer is A. ((x+8)2 ). (x-2 +16x+64=(x+8)2 ). In exams, identify it using \(2\cdot8x=16x\).
Step 3
Exam Tip
(x-2 +16x+64=(x+8)2 ) है। परीक्षा में \(2\cdot8x=16x\) से पहचान करें।
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Question
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
पूर्ण वर्ग विधि में \(x^2+16x+11=0\) के लिए किस संख्या का प्रयोग होगा?
In completing square method for \(x^2+16x+11=0\), which number will be used?
#quadratic
#completing-square
#number-choice
A (64)
B (16)
C (8)
D (11)
Explanation opens after your attempt
Step 1
Concept
Half of (16) is (8), and \(8^2=64\). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. (64). Half of (16) is (8), and \(8^2=64\). In exams, add the square of half the coefficient.
Step 3
Exam Tip
(16) का आधा (8) है और \(8^2=64\) होता है। परीक्षा में आधे गुणांक का वर्ग जोड़ना होता है।
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Question
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
पूर्ण वर्ग बनाते समय \(x^2-18x\) में कौनसा पद जोड़ना होगा?
While completing the square, which term must be added to \(x^2-18x\)?
#quadratic
#completing-square
#term
A (81)
B (18)
C (9)
D (36)
Explanation opens after your attempt
Step 1
Concept
Half of (-18) is (-9), and ((-9)2 =81). In exams, the square of half the coefficient is always positive.
Step 2
Why this answer is correct
The correct answer is A. (81). Half of (-18) is (-9), and ((-9)2 =81). In exams, the square of half the coefficient is always positive.
Step 3
Exam Tip
(-18) का आधा (-9) है और ((-9)2 =81) होता है। परीक्षा में आधे गुणांक का वर्ग हमेशा धनात्मक होता है।
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Question
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
पूर्ण वर्ग विधि में \(x^2+12x+7=0\) के लिए कौनसी संख्या जोड़ी और घटाई जाएगी?
In completing square method for \(x^2+12x+7=0\), which number will be added and subtracted?
#quadratic
#completing-square
#number-choice
A (36)
B (12)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
Half of (12) is (6), and \(6^2=36\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 2
Why this answer is correct
The correct answer is A. (36). Half of (12) is (6), and \(6^2=36\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 3
Exam Tip
(12) का आधा (6) है और \(6^2=36\) होता है। परीक्षा में (\left\(\frac{b}{2}\right\)2 ) का प्रयोग करें।
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Question
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(x^2-10x+25\) किसके बराबर है?
What is \(x^2-10x+25\) equal to?
#quadratic
#perfect-square
#completing-square
A ((x-5)2 )
B ((x+5)2 )
C ((x-10)2 )
D ((x+10)2 )
Explanation opens after your attempt
Correct Answer
A. ((x-5)2 )
Step 1
Concept
(x-2 -10x+25=(x-5)2 ). In exams, check the pattern using \(-2\cdot5x=-10x\).
Step 2
Why this answer is correct
The correct answer is A. ((x-5)2 ). (x-2 -10x+25=(x-5)2 ). In exams, check the pattern using \(-2\cdot5x=-10x\).
Step 3
Exam Tip
(x-2 -10x+25=(x-5)2 ) है। परीक्षा में \(-2\cdot5x=-10x\) से पैटर्न जांचें।
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Question
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
पूर्ण वर्ग विधि में \(x^2-10x+7=0\) के लिए किस संख्या का प्रयोग होगा?
In completing square method for \(x^2-10x+7=0\), which number will be used?
#quadratic
#completing-square
#number-choice
A (25)
B (10)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
Half of (-10) is (-5), and ((-5)2 =25). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. (25). Half of (-10) is (-5), and ((-5)2 =25). In exams, add the square of half the coefficient.
Step 3
Exam Tip
(-10) का आधा (-5) है और ((-5)2 =25) होता है। परीक्षा में आधे गुणांक का वर्ग जोड़ें।
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Question
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
पूर्ण वर्ग बनाकर \(x^2+8x=0\) में \(x^2+8x+16\) किसके बराबर होगा?
By completing the square in \(x^2+8x=0\), what is \(x^2+8x+16\) equal to?
#quadratic
#completing-square
#perfect-square
A ((x+4)2 )
B ((x+8)2 )
C ((x-4)2 )
D ((x+16)2 )
Explanation opens after your attempt
Correct Answer
A. ((x+4)2 )
Step 1
Concept
(x-2 +8x+16=(x+4)2 ). In exams, take half of (8), which is (4), and add its square.
Step 2
Why this answer is correct
The correct answer is A. ((x+4)2 ). (x-2 +8x+16=(x+4)2 ). In exams, take half of (8), which is (4), and add its square.
Step 3
Exam Tip
(x-2 +8x+16=(x+4)2 ) होता है। परीक्षा में (8) का आधा (4) लेकर उसका वर्ग जोड़ें।
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Question
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
पूर्ण वर्ग विधि में \(x^2+6x+5=0\) के लिए किस संख्या को जोड़कर घटाया जाता है?
In completing square method for \(x^2+6x+5=0\), which number is added and subtracted?
#quadratic
#completing-square
#method
A (9)
B (6)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
Half of the coefficient (6) is (3), and \(3^2=9\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 2
Why this answer is correct
The correct answer is A. (9). Half of the coefficient (6) is (3), and \(3^2=9\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 3
Exam Tip
(x) के गुणांक (6) का आधा (3) है और \(3^2=9\) होता है। परीक्षा में (\left\(\frac{b}{2}\right\)2 ) का प्रयोग करें।
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