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completing-square MCQ Questions for Class 10

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73 questions tagged with completing-square.

Question 31/73 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?

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 32/73 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 \(2x^2-4x+5=0\)?

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 33/73 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 \(x^2+4x+1=0\)?

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 34/73 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?

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 35/73 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?

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 36/73 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?

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 37/73 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?

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 38/73 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 \(x^2-6x+18=0\)?

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 39/73 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 \(x^2+8x-33=0\)?

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 40/73 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?

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 41/73 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 \(x^2-18x+45=0\)?

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 42/73 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?

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 43/73 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?

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 44/73 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?

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 45/73 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?

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 46/73 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 \(x^2-4x+13=0\)?

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 47/73 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 \(x^2+2x-24=0\)?

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 48/73 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?

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 49/73 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 \(x^2-16x+28=0\)?

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 50/73 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?

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 51/73 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?

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 52/73 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?

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 53/73 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?

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 54/73 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 \(x^2-2x+5=0\)?

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 55/73 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 \(x^2+4x-12=0\)?

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 56/73 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?

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 57/73 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 \(x^2-12x+20=0\)?

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 58/73 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?

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 59/73 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?

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 60/73 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?

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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