\(2x^2-7x+3=0\) को गुणनखंड विधि से हल करने पर मूल क्या हैं?
What are the roots of \(2x^2-7x+3=0\) by factorisation method?
#quadratic
#factorisation
#medium
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x=3,\frac{1}{2}\)
B \(x=-3,-\frac{1}{2}\)
C (x=2,3)
D \(x=\frac{3}{2},1\)
Explanation opens after your attempt
Correct Answer
A. \(x=3,\frac{1}{2}\)
Step 1
Concept
(2x-2 -7x+3=(2x-1)(x-3)), so (x=3) and \(x=\frac{1}{2}\). In exams, solve each linear factor separately.
Step 2
Why this answer is correct
The correct answer is A. \(x=3,\frac{1}{2}\). (2x-2 -7x+3=(2x-1)(x-3)), so (x=3) and \(x=\frac{1}{2}\). In exams, solve each linear factor separately.
Step 3
Exam Tip
(2x-2 -7x+3=(2x-1)(x-3)), इसलिए (x=3) और \(x=\frac{1}{2}\) हैं। परीक्षा में रैखिक गुणनखंड को अलग-अलग हल करें।
Login to save your score, XP, coins and progress. Login
\(6x^2+11x+3=0\) में मध्य पद का सही विभाजन कौनसा है?
What is the correct splitting of the middle term in \(6x^2+11x+3=0\)?
#quadratic
#middle-term-splitting
#ac-method
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(6x^2+9x+2x+3=0\)
B \(6x^2+8x+3x+3=0\)
C \(6x^2+6x+5x+3=0\)
D \(6x^2+12x-x+3=0\)
Explanation opens after your attempt
Correct Answer
A. \(6x^2+9x+2x+3=0\)
Step 1
Concept
Here (ac=18) and (9+2=11), so (11x) is split as (9x+2x). In exams, check both sum (b) and product (ac).
Step 2
Why this answer is correct
The correct answer is A. \(6x^2+9x+2x+3=0\). Here (ac=18) and (9+2=11), so (11x) is split as (9x+2x). In exams, check both sum (b) and product (ac).
Step 3
Exam Tip
यहां (ac=18) और (9+2=11), इसलिए (11x) को (9x+2x) में तोड़ते हैं। परीक्षा में योग (b) और गुणनफल (ac) दोनों जांचें।
Login to save your score, XP, coins and progress. Login
\(3x^2-2x-1=0\) के मूल कौनसे हैं?
Which are the roots of \(3x^2-2x-1=0\)?
#quadratic
#factorisation
#fraction-roots
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x=1,-\frac{1}{3}\)
B \(x=-1,\frac{1}{3}\)
C (x=3,-1)
D \(x=\frac{1}{3},-1\)
Explanation opens after your attempt
Correct Answer
A. \(x=1,-\frac{1}{3}\)
Step 1
Concept
(3x-2 -2x-1=(3x+1)(x-1)), so the roots are (1) and \(-\frac{1}{3}\). In exams, form mixed-sign factors carefully.
Step 2
Why this answer is correct
The correct answer is A. \(x=1,-\frac{1}{3}\). (3x-2 -2x-1=(3x+1)(x-1)), so the roots are (1) and \(-\frac{1}{3}\). In exams, form mixed-sign factors carefully.
Step 3
Exam Tip
(3x-2 -2x-1=(3x+1)(x-1)), इसलिए मूल (1) और \(-\frac{1}{3}\) हैं। परीक्षा में मिश्रित चिन्ह वाले गुणनखंड सावधानी से बनाएं।
Login to save your score, XP, coins and progress. Login
\(x^2-2x-15=0\) को हल करने के लिए सही गुणनखंड रूप क्या है?
What is the correct factorised form to solve \(x^2-2x-15=0\)?
#quadratic
#factorisation
#mixed-signs
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ((x-5)(x+3)=0)
B ((x+5)(x-3)=0)
C ((x-15)(x+1)=0)
D ((x+15)(x-1)=0)
Explanation opens after your attempt
Correct Answer
A. ((x-5)(x+3)=0)
Step 1
Concept
(-5+3=-2) and \(-5\times3=-15\), so ((x-5)(x+3)) is correct. In exams, match both product and sum.
Step 2
Why this answer is correct
The correct answer is A. ((x-5)(x+3)=0). (-5+3=-2) and \(-5\times3=-15\), so ((x-5)(x+3)) is correct. In exams, match both product and sum.
Step 3
Exam Tip
(-5+3=-2) और \(-5\times3=-15\), इसलिए ((x-5)(x+3)) सही है। परीक्षा में गुणनफल और योग दोनों मिलाएं।
Login to save your score, XP, coins and progress. Login
द्विघात सूत्र से \(x^2-4x-5=0\) के मूल क्या मिलेंगे?
Using the quadratic formula, what roots are obtained for \(x^2-4x-5=0\)?
#quadratic
#quadratic-formula
#roots
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x=5,-1)
B (x=-5,1)
C (x=4,-5)
D (x=2,-3)
Explanation opens after your attempt
Correct Answer
A. (x=5,-1)
Step 1
Concept
Here (D=(-4)2 -4(1)(-5)=36), so \(x=\frac{4\pm6}{2}\). In exams, do not forget the negative sign of (c) while using the formula.
Step 2
Why this answer is correct
The correct answer is A. (x=5,-1). Here (D=(-4)2 -4(1)(-5)=36), so \(x=\frac{4\pm6}{2}\). In exams, do not forget the negative sign of (c) while using the formula.
Step 3
Exam Tip
यहां (D=(-4)2 -4(1)(-5)=36), इसलिए \(x=\frac{4\pm6}{2}\) मिलता है। परीक्षा में सूत्र लगाते समय (c) का ऋण चिन्ह न भूलें।
Login to save your score, XP, coins and progress. Login
\(x^2+6x+1=0\) 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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
\(x^2+6x+1=0\) 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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
यदि \(2x^2+5x=3\) है, तो मानक रूप \(ax^2+bx+c=0\) में (a,b,c) क्या हैं?
If \(2x^2+5x=3\), what are (a,b,c) in standard form \(ax^2+bx+c=0\)?
#quadratic
#standard-form
#coefficients
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (a=2,b=5,c=-3)
B (a=2,b=5,c=3)
C (a=5,b=2,c=-3)
D (a=2,b=-5,c=3)
Explanation opens after your attempt
Correct Answer
A. (a=2,b=5,c=-3)
Step 1
Concept
The standard form is \(2x^2+5x-3=0\), so (a=2,b=5,c=-3). In exams, bring all terms to one side first.
Step 2
Why this answer is correct
The correct answer is A. (a=2,b=5,c=-3). The standard form is \(2x^2+5x-3=0\), so (a=2,b=5,c=-3). In exams, bring all terms to one side first.
Step 3
Exam Tip
मानक रूप \(2x^2+5x-3=0\) है, इसलिए (a=2,b=5,c=-3) हैं। परीक्षा में सभी पदों को पहले एक तरफ लाएं।
Login to save your score, XP, coins and progress. Login
\(2x^2+5x-3=0\) के मूल क्या हैं?
What are the roots of \(2x^2+5x-3=0\)?
#quadratic
#factorisation
#standard-form
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x=\frac{1}{2},-3\)
B \(x=-\frac{1}{2},3\)
C (x=2,-3)
D \(x=3,-\frac{1}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{1}{2},-3\)
Step 1
Concept
(2x-2 +5x-3=(2x-1)(x+3)), so \(x=\frac{1}{2}\) and (-3). In exams, write fractional roots correctly.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{1}{2},-3\). (2x-2 +5x-3=(2x-1)(x+3)), so \(x=\frac{1}{2}\) and (-3). In exams, write fractional roots correctly.
Step 3
Exam Tip
(2x-2 +5x-3=(2x-1)(x+3)), इसलिए \(x=\frac{1}{2}\) और (-3) हैं। परीक्षा में भिन्न मूल को सही लिखें।
Login to save your score, XP, coins and progress. Login
\(4x^2-12x+9=0\) किस पूर्ण वर्ग रूप में लिखा जाएगा?
In which perfect square form will \(4x^2-12x+9=0\) be written?
#quadratic
#perfect-square
#factorisation
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ((2x-3)2 =0)
B ((2x+3)2 =0)
C ((4x-3)2 =0)
D ((x-3)2 =0)
Explanation opens after your attempt
Correct Answer
A. ((2x-3)2 =0)
Step 1
Concept
(4x-2 -12x+9=(2x-3)2 ), so it is a perfect square. In exams, recognize the pattern ((a-b)2 ).
Step 2
Why this answer is correct
The correct answer is A. ((2x-3)2 =0). (4x-2 -12x+9=(2x-3)2 ), so it is a perfect square. In exams, recognize the pattern ((a-b)2 ).
Step 3
Exam Tip
(4x-2 -12x+9=(2x-3)2 ), इसलिए यह पूर्ण वर्ग है। परीक्षा में ((a-b)2 ) का पैटर्न पहचानें।
Login to save your score, XP, coins and progress. Login
\(4x^2-12x+9=0\) का दोहराया हुआ मूल क्या है?
What is the repeated root of \(4x^2-12x+9=0\)?
#quadratic
#repeated-root
#perfect-square
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x=\frac{3}{2}\)
B \(x=-\frac{3}{2}\)
C (x=3)
D \(x=\frac{2}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{3}{2}\)
Step 1
Concept
((2x-3)2 =0), so (2x-3=0) and \(x=\frac{3}{2}\). In exams, write the repeated root with the correct value.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{3}{2}\). ((2x-3)2 =0), so (2x-3=0) and \(x=\frac{3}{2}\). In exams, write the repeated root with the correct value.
Step 3
Exam Tip
((2x-3)2 =0), इसलिए (2x-3=0) और \(x=\frac{3}{2}\) है। परीक्षा में दोहराए हुए मूल को भी सही मान से लिखें।
Login to save your score, XP, coins and progress. Login
\(5x^2-20x=0\) को हल करते समय कौनसी सामान्य गलती हो सकती है?
What common mistake can occur while solving \(5x^2-20x=0\)?
#quadratic
#common-mistake
#zero-root
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x=0) को छोड़ देना / Missing (x=0)
B (x=4) को लिखना / Writing (x=4)
C (5x) सामान्य गुणनखंड लेना / Taking (5x) common
D (5x(x-4)=0) लिखना / Writing (5x(x-4)=0)
Explanation opens after your attempt
Correct Answer
A. (x=0) को छोड़ देना / Missing (x=0)
Step 1
Concept
The correct form is (5x(x-4)=0), giving (x=0) and (x=4). In exams, dividing directly by the variable can miss (x=0).
Step 2
Why this answer is correct
The correct answer is A. (x=0) को छोड़ देना / Missing (x=0). The correct form is (5x(x-4)=0), giving (x=0) and (x=4). In exams, dividing directly by the variable can miss (x=0).
Step 3
Exam Tip
सही रूप (5x(x-4)=0) है, जिससे (x=0) और (x=4) मिलते हैं। परीक्षा में चर से सीधे भाग देने से (x=0) छूट सकता है।
Login to save your score, XP, coins and progress. Login
\(3x^2+5x-2=0\) को गुणनखंड विधि से हल करने पर मूल क्या होंगे?
What roots are obtained by solving \(3x^2+5x-2=0\) by factorisation?
#quadratic
#factorisation
#fraction-roots
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x=\frac{1}{3},-2\)
B \(x=-\frac{1}{3},2\)
C (x=3,-2)
D \(x=\frac{2}{3},-1\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{1}{3},-2\)
Step 1
Concept
(3x-2 +5x-2=(3x-1)(x+2)), so the roots are \(\frac{1}{3}\) and (-2). In exams, solve (3x-1=0) carefully.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{1}{3},-2\). (3x-2 +5x-2=(3x-1)(x+2)), so the roots are \(\frac{1}{3}\) and (-2). In exams, solve (3x-1=0) carefully.
Step 3
Exam Tip
(3x-2 +5x-2=(3x-1)(x+2)), इसलिए मूल \(\frac{1}{3}\) और (-2) हैं। परीक्षा में (3x-1=0) को सावधानी से हल करें।
Login to save your score, XP, coins and progress. Login
द्विघात सूत्र से \(2x^2-4x-3=0\) के लिए (D) का मान क्या है?
Using the quadratic formula setup, what is the value of (D) for \(2x^2-4x-3=0\)?
#quadratic
#discriminant
#calculation
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (40)
B (16)
C (24)
D (8)
Explanation opens after your attempt
Step 1
Concept
Here (D=(-4)2 -4(2)(-3)=40). In exams, a negative (c) makes the term add.
Step 2
Why this answer is correct
The correct answer is A. (40). Here (D=(-4)2 -4(2)(-3)=40). In exams, a negative (c) makes the term add.
Step 3
Exam Tip
यहां (D=(-4)2 -4(2)(-3)=40) है। परीक्षा में ऋणात्मक (c) के कारण जोड़ बनता है।
Login to save your score, XP, coins and progress. Login
\(2x^2-4x-3=0\) के मूलों का सही रूप क्या है?
What is the correct form of the roots of \(2x^2-4x-3=0\)?
#quadratic
#quadratic-formula
#irrational-roots
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x=1\pm\frac{\sqrt{10}}{2}\)
B \(x=2\pm\sqrt{10}\)
C \(x=1\pm\sqrt{10}\)
D \(x=\frac{1\pm\sqrt{10}}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(x=1\pm\frac{\sqrt{10}}{2}\)
Step 1
Concept
The formula gives \(x=\frac{4\pm\sqrt{40}}{4}=1\pm\frac{\sqrt{10}}{2}\). In exams, simplify the final form.
Step 2
Why this answer is correct
The correct answer is A. \(x=1\pm\frac{\sqrt{10}}{2}\). The formula gives \(x=\frac{4\pm\sqrt{40}}{4}=1\pm\frac{\sqrt{10}}{2}\). In exams, simplify the final form.
Step 3
Exam Tip
सूत्र से \(x=\frac{4\pm\sqrt{40}}{4}=1\pm\frac{\sqrt{10}}{2}\) मिलता है। परीक्षा में अंतिम रूप को सरल करें।
Login to save your score, XP, coins and progress. Login
यदि \(x^2-10x+k=0\) के मूल समान हों, तो (k) का मान क्या होगा?
If \(x^2-10x+k=0\) has equal roots, what is the value of (k)?
#quadratic
#discriminant
#parameter
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (25)
B (10)
C (20)
D (100)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (100-4k=0) and (k=25). In exams, equal roots indicate (D=0).
Step 2
Why this answer is correct
The correct answer is A. (25). For equal roots, (D=0), so (100-4k=0) and (k=25). In exams, equal roots indicate (D=0).
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (100-4k=0) और (k=25) है। परीक्षा में समान मूल का संकेत (D=0) होता है।
Login to save your score, XP, coins and progress. Login
यदि \(x^2+kx+16=0\) के समान मूल हैं और (k>0), तो (k) क्या होगा?
If \(x^2+kx+16=0\) has equal roots and (k>0), what is (k)?
#quadratic
#discriminant
#parameter
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (8)
B (4)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
For equal roots, \(k^2-64=0\), so \(k=\pm8\), and (k>0) gives (k=8). In exams, apply the given condition.
Step 2
Why this answer is correct
The correct answer is A. (8). For equal roots, \(k^2-64=0\), so \(k=\pm8\), and (k>0) gives (k=8). In exams, apply the given condition.
Step 3
Exam Tip
समान मूलों के लिए \(k^2-64=0\), इसलिए \(k=\pm8\) और (k>0) से (k=8) है। परीक्षा में दी गई शर्त जरूर लगाएं।
Login to save your score, XP, coins and progress. Login
\(x^2-5x+6=0\) और \(x^2-6x+8=0\) में कौनसा मूल समान है?
Which root is common to \(x^2-5x+6=0\) and \(x^2-6x+8=0\)?
#quadratic
#common-root
#factorisation
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x=2)
B (x=3)
C (x=4)
D (x=6)
Explanation opens after your attempt
Step 1
Concept
The roots of the first equation are (2,3), and the roots of the second are (2,4). In exams, solve both equations separately and compare roots.
Step 2
Why this answer is correct
The correct answer is A. (x=2). The roots of the first equation are (2,3), and the roots of the second are (2,4). In exams, solve both equations separately and compare roots.
Step 3
Exam Tip
पहले समीकरण के मूल (2,3) और दूसरे के मूल (2,4) हैं। परीक्षा में दोनों समीकरण अलग-अलग हल करके समान मूल देखें।
Login to save your score, XP, coins and progress. Login
किस समीकरण को पहले (x) से भाग करना सुरक्षित नहीं है?
For which equation is it not safe to divide by (x) first?
#quadratic
#common-mistake
#division-by-variable
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x^2-8x=0\)
B \(x^2-8=0\)
C \(x^2+8=0\)
D \(x^2-64=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-8x=0\)
Step 1
Concept
In \(x^2-8x=0\), (x) is a common factor and (x=0) can be a root. In exams, write (x(x-8)=0) in such cases.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-8x=0\). In \(x^2-8x=0\), (x) is a common factor and (x=0) can be a root. In exams, write (x(x-8)=0) in such cases.
Step 3
Exam Tip
\(x^2-8x=0\) में (x) सामान्य गुणनखंड है और (x=0) मूल हो सकता है। परीक्षा में ऐसे मामलों में (x(x-8)=0) लिखें।
Login to save your score, XP, coins and progress. Login
\(9x^2-30x+25=0\) को किस पूर्ण वर्ग रूप में लिखा जाएगा?
In which perfect square form will \(9x^2-30x+25=0\) be written?
#quadratic
#perfect-square
#identity
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ((3x-5)2 =0)
B ((3x+5)2 =0)
C ((9x-5)2 =0)
D ((x-5)2 =0)
Explanation opens after your attempt
Correct Answer
A. ((3x-5)2 =0)
Step 1
Concept
(9x-2 -30x+25=(3x-5)2 ). In exams, check the pattern using \(2\cdot3x\cdot5=30x\).
Step 2
Why this answer is correct
The correct answer is A. ((3x-5)2 =0). (9x-2 -30x+25=(3x-5)2 ). In exams, check the pattern using \(2\cdot3x\cdot5=30x\).
Step 3
Exam Tip
(9x-2 -30x+25=(3x-5)2 ) है। परीक्षा में \(2\cdot3x\cdot5=30x\) से पैटर्न जांचें।
Login to save your score, XP, coins and progress. Login
\(9x^2-30x+25=0\) का मूल क्या है?
What is the root of \(9x^2-30x+25=0\)?
#quadratic
#repeated-root
#perfect-square
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x=\frac{5}{3}\)
B \(x=-\frac{5}{3}\)
C \(x=\frac{3}{5}\)
D (x=5)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{5}{3}\)
Step 1
Concept
((3x-5)2 =0), so (3x-5=0) and \(x=\frac{5}{3}\). In exams, solve the linear equation after square form.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{5}{3}\). ((3x-5)2 =0), so (3x-5=0) and \(x=\frac{5}{3}\). In exams, solve the linear equation after square form.
Step 3
Exam Tip
((3x-5)2 =0), इसलिए (3x-5=0) और \(x=\frac{5}{3}\) है। परीक्षा में वर्ग रूप के बाद रैखिक समीकरण हल करें।
Login to save your score, XP, coins and progress. Login
\(4x^2-1=8x\) को मानक रूप में लिखने पर क्या मिलेगा?
What is obtained when \(4x^2-1=8x\) is written in standard form?
#quadratic
#standard-form
#transposition
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(4x^2-8x-1=0\)
B \(4x^2+8x-1=0\)
C \(4x^2-8x+1=0\)
D \(4x^2-1=0\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2-8x-1=0\)
Step 1
Concept
Bringing (8x) to the left gives \(4x^2-8x-1=0\). In exams, do not miss any term while making standard form.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2-8x-1=0\). Bringing (8x) to the left gives \(4x^2-8x-1=0\). In exams, do not miss any term while making standard form.
Step 3
Exam Tip
(8x) को बाईं तरफ लाने पर \(4x^2-8x-1=0\) बनता है। परीक्षा में मानक रूप बनाने से पहले कोई पद न छोड़ें।
Login to save your score, XP, coins and progress. Login
\(4x^2-8x-1=0\) का विविक्तकर (D) क्या है?
What is the discriminant (D) of \(4x^2-8x-1=0\)?
#quadratic
#discriminant
#calculation
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (80)
B (64)
C (48)
D (16)
Explanation opens after your attempt
Step 1
Concept
Here (D=(-8)2 -4(4)(-1)=80). In exams, a negative (c) increases (D).
Step 2
Why this answer is correct
The correct answer is A. (80). Here (D=(-8)2 -4(4)(-1)=80). In exams, a negative (c) increases (D).
Step 3
Exam Tip
यहां (D=(-8)2 -4(4)(-1)=80) है। परीक्षा में ऋणात्मक (c) से (D) बढ़ जाता है।
Login to save your score, XP, coins and progress. Login
\(x^2-12x+20=0\) 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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
\(x^2-12x+20=0\) के मूल क्या हैं?
What are the roots of \(x^2-12x+20=0\)?
#quadratic
#completing-square
#roots
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
यदि \(x^2+px+12=0\) के मूल (-3) और (-4) हैं, तो (p) क्या है?
If the roots of \(x^2+px+12=0\) are (-3) and (-4), what is (p)?
#quadratic
#roots-to-equation
#parameter
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (7)
B (-7)
C (12)
D (1)
Explanation opens after your attempt
Step 1
Concept
((x+3)(x+4)=x-2 +7x+12), so (p=7). In exams, form factors from given roots.
Step 2
Why this answer is correct
The correct answer is A. (7). ((x+3)(x+4)=x-2 +7x+12), so (p=7). In exams, form factors from given roots.
Step 3
Exam Tip
((x+3)(x+4)=x-2 +7x+12), इसलिए (p=7) है। परीक्षा में दिए हुए मूलों से गुणनखंड बनाएं।
Login to save your score, XP, coins and progress. Login
यदि (2) और (5) किसी द्विघात समीकरण के मूल हैं, तो वह समीकरण कौनसा हो सकता है?
If (2) and (5) are roots of a quadratic equation, which equation can it be?
#quadratic
#construct-equation
#roots
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x^2-7x+10=0\)
B \(x^2+7x+10=0\)
C \(x^2-10x+7=0\)
D \(x^2+10x+7=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-7x+10=0\)
Step 1
Concept
If the roots are (2) and (5), the equation is ((x-2)(x-5)=0), that is \(x^2-7x+10=0\). In exams, form factors with opposite signs of roots.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-7x+10=0\). If the roots are (2) and (5), the equation is ((x-2)(x-5)=0), that is \(x^2-7x+10=0\). In exams, form factors with opposite signs of roots.
Step 3
Exam Tip
मूल (2) और (5) हों तो समीकरण ((x-2)(x-5)=0) यानी \(x^2-7x+10=0\) है। परीक्षा में मूलों के विपरीत चिन्ह से गुणनखंड बनाएं।
Login to save your score, XP, coins and progress. Login
\(2x^2+7x+6=0\) को हल करने पर मूल क्या होंगे?
What will be the roots after solving \(2x^2+7x+6=0\)?
#quadratic
#factorisation
#fraction-roots
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x=-\frac{3}{2},-2\)
B \(x=\frac{3}{2},2\)
C \(x=-3,-\frac{1}{2}\)
D (x=-1,-6)
Explanation opens after your attempt
Correct Answer
A. \(x=-\frac{3}{2},-2\)
Step 1
Concept
(2x-2 +7x+6=(2x+3)(x+2)), so \(x=-\frac{3}{2}\) and (-2). In exams, positive factors give negative roots.
Step 2
Why this answer is correct
The correct answer is A. \(x=-\frac{3}{2},-2\). (2x-2 +7x+6=(2x+3)(x+2)), so \(x=-\frac{3}{2}\) and (-2). In exams, positive factors give negative roots.
Step 3
Exam Tip
(2x-2 +7x+6=(2x+3)(x+2)), इसलिए \(x=-\frac{3}{2}\) और (-2) हैं। परीक्षा में धनात्मक गुणनखंडों से ऋणात्मक मूल मिलते हैं।
Login to save your score, XP, coins and progress. Login
\(x^2-3x-10=0\) के लिए निम्न में से कौनसा कथन सही है?
Which statement is correct for \(x^2-3x-10=0\)?
#quadratic
#roots
#mixed-signs
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A मूल (5) और (-2) हैं / The roots are (5) and (-2)
B मूल (-5) और (2) हैं / The roots are (-5) and (2)
C मूल (3) और (10) हैं / The roots are (3) and (10)
D मूल (-3) और (-10) हैं / The roots are (-3) and (-10)
Explanation opens after your attempt
Correct Answer
A. मूल (5) और (-2) हैं / The roots are (5) and (-2)
Step 1
Concept
(x-2 -3x-10=(x-5)(x+2)), so the roots are (5) and (-2). In exams, in mixed signs the larger value decides the middle-term sign.
Step 2
Why this answer is correct
The correct answer is A. मूल (5) और (-2) हैं / The roots are (5) and (-2). (x-2 -3x-10=(x-5)(x+2)), so the roots are (5) and (-2). In exams, in mixed signs the larger value decides the middle-term sign.
Step 3
Exam Tip
(x-2 -3x-10=(x-5)(x+2)), इसलिए मूल (5) और (-2) हैं। परीक्षा में मिश्रित चिन्हों में बड़ा मान मध्य पद का चिन्ह तय करता है।
Login to save your score, XP, coins and progress. Login
द्विघात सूत्र में (a=1,b=-6,c=8) रखने पर मूल क्या होंगे?
What roots are obtained by putting (a=1,b=-6,c=8) in the quadratic formula?
#quadratic
#quadratic-formula
#substitution
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x=2,4)
B (x=-2,-4)
C (x=1,8)
D (x=6,8)
Explanation opens after your attempt
Correct Answer
A. (x=2,4)
Step 1
Concept
(D=(-6)2 -4(1)(8)=4), so \(x=\frac{6\pm2}{2}\) gives (2) and (4). In exams, keep the sign of (-b) correct.
Step 2
Why this answer is correct
The correct answer is A. (x=2,4). (D=(-6)2 -4(1)(8)=4), so \(x=\frac{6\pm2}{2}\) gives (2) and (4). In exams, keep the sign of (-b) correct.
Step 3
Exam Tip
(D=(-6)2 -4(1)(8)=4), इसलिए \(x=\frac{6\pm2}{2}\) से (2) और (4) मिलते हैं। परीक्षा में (-b) का चिन्ह सही रखें।
Login to save your score, XP, coins and progress. Login
\(x^2-14x+45=0\) में कौनसी संख्या जोड़ी मध्य पद बनाने में मदद करेगी?
Which number pair helps in making the middle term in \(x^2-14x+45=0\)?
#quadratic
#middle-term-splitting
#signs
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (-5) और (-9) / (-5) and (-9)
B (5) और (9) / (5) and (9)
C (-3) और (-15) / (-3) and (-15)
D (3) और (15) / (3) and (15)
Explanation opens after your attempt
Correct Answer
A. (-5) और (-9) / (-5) and (-9)
Step 1
Concept
(-5+(-9)=-14) and ((-5)(-9)=45), so this pair is correct. In exams, if (c) is positive and (b) is negative, both numbers may be negative.
Step 2
Why this answer is correct
The correct answer is A. (-5) और (-9) / (-5) and (-9). (-5+(-9)=-14) and ((-5)(-9)=45), so this pair is correct. In exams, if (c) is positive and (b) is negative, both numbers may be negative.
Step 3
Exam Tip
(-5+(-9)=-14) और ((-5)(-9)=45), इसलिए यह जोड़ी सही है। परीक्षा में (c) धनात्मक और (b) ऋणात्मक हो तो दोनों संख्याएं ऋणात्मक हो सकती हैं।
Login to save your score, XP, coins and progress. Login
\(7x^2=28x\) को हल करने का सही तरीका क्या है?
What is the correct way to solve \(7x^2=28x\)?
#quadratic
#common-factor
#zero-product
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (7x(x-4)=0) लिखना / Write (7x(x-4)=0)
B (x=4) ही लिखना / Write only (x=4)
C (7x=28) लिखना / Write (7x=28)
D \(x^2=4x\) के बाद (x=4) ही लेना / After \(x^2=4x\), take only (x=4)
Explanation opens after your attempt
Correct Answer
A. (7x(x-4)=0) लिखना / Write (7x(x-4)=0)
Step 1
Concept
From \(7x^2-28x=0\), (7x(x-4)=0), so (x=0) and (x=4). In exams, dividing by the variable can miss one root.
Step 2
Why this answer is correct
The correct answer is A. (7x(x-4)=0) लिखना / Write (7x(x-4)=0). From \(7x^2-28x=0\), (7x(x-4)=0), so (x=0) and (x=4). In exams, dividing by the variable can miss one root.
Step 3
Exam Tip
\(7x^2-28x=0\) से (7x(x-4)=0), इसलिए (x=0) और (x=4) हैं। परीक्षा में चर से भाग देने से एक मूल छूट सकता है।
Login to save your score, XP, coins and progress. Login
\(x^2+4x-12=0\) 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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
\(x^2+4x-12=0\) के मूल क्या हैं?
What are the roots of \(x^2+4x-12=0\)?
#quadratic
#completing-square
#roots
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
\(2x^2+x-6=0\) में मध्य पद का सही विभाजन कौनसा है?
What is the correct splitting of the middle term in \(2x^2+x-6=0\)?
#quadratic
#middle-term-splitting
#ac-method
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(2x^2+4x-3x-6=0\)
B \(2x^2+3x-2x-6=0\)
C \(2x^2+6x-5x-6=0\)
D \(2x^2-4x+5x-6=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+4x-3x-6=0\)
Step 1
Concept
(ac=-12) and (4+(-3)=1), so (x) is split as (4x-3x). In exams, check the sign of (ac) carefully.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+4x-3x-6=0\). (ac=-12) and (4+(-3)=1), so (x) is split as (4x-3x). In exams, check the sign of (ac) carefully.
Step 3
Exam Tip
(ac=-12) और (4+(-3)=1), इसलिए (x) को (4x-3x) में तोड़ते हैं। परीक्षा में (ac) का संकेत ध्यान से देखें।
Login to save your score, XP, coins and progress. Login
यदि (D=0) और (a=2,b=-8), तो समान मूल क्या होगा?
If (D=0) and (a=2,b=-8), what will be the equal root?
#quadratic
#equal-roots
#formula
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x=2)
B (x=-2)
C (x=4)
D (x=-4)
Explanation opens after your attempt
Step 1
Concept
The equal root is \(x=\frac{-b}{2a}\), so \(x=\frac{8}{4}=2\). In exams, this short formula is useful when (D=0).
Step 2
Why this answer is correct
The correct answer is A. (x=2). The equal root is \(x=\frac{-b}{2a}\), so \(x=\frac{8}{4}=2\). In exams, this short formula is useful when (D=0).
Step 3
Exam Tip
समान मूल \(x=\frac{-b}{2a}\) होता है, इसलिए \(x=\frac{8}{4}=2\) है। परीक्षा में (D=0) पर यह छोटा सूत्र उपयोगी है।
Login to save your score, XP, coins and progress. Login
\(x^2-2x+5=0\) के वास्तविक मूलों के बारे में सही कथन क्या है?
What is the correct statement about real roots of \(x^2-2x+5=0\)?
#quadratic
#discriminant
#no-real-roots
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A कोई वास्तविक मूल नहीं / No real roots
B दो समान वास्तविक मूल / Two equal real roots
C दो अलग वास्तविक मूल / Two distinct real roots
D एक मूल (0) / One root (0)
Explanation opens after your attempt
Correct Answer
A. कोई वास्तविक मूल नहीं / No real roots
Step 1
Concept
Here (D=(-2)2 -4(1)(5)=-16<0), so there are no real roots. In exams, (D<0) means no real solution.
Step 2
Why this answer is correct
The correct answer is A. कोई वास्तविक मूल नहीं / No real roots. Here (D=(-2)2 -4(1)(5)=-16<0), so there are no real roots. In exams, (D<0) means no real solution.
Step 3
Exam Tip
यहां (D=(-2)2 -4(1)(5)=-16<0), इसलिए वास्तविक मूल नहीं हैं। परीक्षा में (D<0) होने पर वास्तविक हल नहीं मिलता।
Login to save your score, XP, coins and progress. Login
\(x^2-2x+5=0\) 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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
\(3x^2=12\) को वर्गमूल विधि से हल करने पर मूल क्या होंगे?
What roots are obtained by solving \(3x^2=12\) by square root method?
#quadratic
#square-root-method
#solutions
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x=\pm2\)
B (x=2)
C (x=-2)
D \(x=\pm4\)
Explanation opens after your attempt
Correct Answer
A. \(x=\pm2\)
Step 1
Concept
First \(x^2=4\), so \(x=\pm2\). In exams, write both signs while taking square root.
Step 2
Why this answer is correct
The correct answer is A. \(x=\pm2\). First \(x^2=4\), so \(x=\pm2\). In exams, write both signs while taking square root.
Step 3
Exam Tip
पहले \(x^2=4\) मिलता है, इसलिए \(x=\pm2\) है। परीक्षा में वर्गमूल लेते समय दोनों चिन्ह लिखें।
Login to save your score, XP, coins and progress. Login
((x-5)2 =3) को हल करने पर (x) का मान क्या होगा?
Solving ((x-5)2 =3), what will be the value of (x)?
#quadratic
#square-root-method
#irrational-roots
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x=5\pm\sqrt{3}\)
B \(x=-5\pm\sqrt{3}\)
C \(x=5\pm3\)
D \(x=\sqrt{5}\pm3\)
Explanation opens after your attempt
Correct Answer
A. \(x=5\pm\sqrt{3}\)
Step 1
Concept
\(x-5=\pm\sqrt{3}\), so \(x=5\pm\sqrt{3}\). In exams, write \(\pm\) with the whole square root.
Step 2
Why this answer is correct
The correct answer is A. \(x=5\pm\sqrt{3}\). \(x-5=\pm\sqrt{3}\), so \(x=5\pm\sqrt{3}\). In exams, write \(\pm\) with the whole square root.
Step 3
Exam Tip
\(x-5=\pm\sqrt{3}\), इसलिए \(x=5\pm\sqrt{3}\) है। परीक्षा में \(\pm\) को पूरे वर्गमूल के साथ लिखें।
Login to save your score, XP, coins and progress. Login
\(x^2+10x+21=0\) के लिए सही हल कौनसा है?
Which is the correct solution for \(x^2+10x+21=0\)?
#quadratic
#factorisation
#sign-concept
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x=-3,-7)
B (x=3,7)
C (x=-10,-21)
D (x=10,21)
Explanation opens after your attempt
Correct Answer
A. (x=-3,-7)
Step 1
Concept
(x-2 +10x+21=(x+3)(x+7)), so (x=-3,-7). In exams, a positive middle term and positive constant can give both negative roots.
Step 2
Why this answer is correct
The correct answer is A. (x=-3,-7). (x-2 +10x+21=(x+3)(x+7)), so (x=-3,-7). In exams, a positive middle term and positive constant can give both negative roots.
Step 3
Exam Tip
(x-2 +10x+21=(x+3)(x+7)), इसलिए (x=-3,-7) हैं। परीक्षा में धनात्मक मध्य पद और धनात्मक स्थिर पद पर दोनों मूल ऋणात्मक हो सकते हैं।
Login to save your score, XP, coins and progress. Login
\(5x^2+6x+1=0\) में कौनसा गुणनखंड रूप सही है?
Which factorised form is correct for \(5x^2+6x+1=0\)?
#quadratic
#factorisation
#verification
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ((5x+1)(x+1)=0)
B ((5x-1)(x-1)=0)
C ((x+5)(x+1)=0)
D ((5x+6)(x+1)=0)
Explanation opens after your attempt
Correct Answer
A. ((5x+1)(x+1)=0)
Step 1
Concept
((5x+1)(x+1)=5x-2 +6x+1), so it is correct. In exams, verify factors by expanding.
Step 2
Why this answer is correct
The correct answer is A. ((5x+1)(x+1)=0). ((5x+1)(x+1)=5x-2 +6x+1), so it is correct. In exams, verify factors by expanding.
Step 3
Exam Tip
((5x+1)(x+1)=5x-2 +6x+1), इसलिए यह सही है। परीक्षा में विस्तार करके गुणनखंड जांचें।
Login to save your score, XP, coins and progress. Login
\(5x^2+6x+1=0\) के मूल क्या होंगे?
What will be the roots of \(5x^2+6x+1=0\)?
#quadratic
#fraction-roots
#zero-product
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x=-\frac{1}{5},-1\)
B \(x=\frac{1}{5},1\)
C (x=-5,-1)
D (x=5,1)
Explanation opens after your attempt
Correct Answer
A. \(x=-\frac{1}{5},-1\)
Step 1
Concept
((5x+1)(x+1)=0), so \(x=-\frac{1}{5}\) and (-1). In exams, ((5x+1)=0) gives \(-\frac{1}{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(x=-\frac{1}{5},-1\). ((5x+1)(x+1)=0), so \(x=-\frac{1}{5}\) and (-1). In exams, ((5x+1)=0) gives \(-\frac{1}{5}\).
Step 3
Exam Tip
((5x+1)(x+1)=0), इसलिए \(x=-\frac{1}{5}\) और (-1) हैं। परीक्षा में ((5x+1)=0) से \(-\frac{1}{5}\) मिलता है।
Login to save your score, XP, coins and progress. Login
किस समीकरण में गुणनखंड विधि की जगह द्विघात सूत्र अधिक सुविधाजनक है?
For which equation is the quadratic formula more convenient than factorisation?
#quadratic
#method-selection
#quadratic-formula
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x^2+x-1=0\)
B \(x^2+5x+6=0\)
C \(x^2-9=0\)
D \(x^2-4x+4=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+x-1=0\)
Step 1
Concept
\(x^2+x-1=0\) has no simple integer factors, so the formula method is easier. In exams, the quadratic formula is safe in such cases.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+x-1=0\). \(x^2+x-1=0\) has no simple integer factors, so the formula method is easier. In exams, the quadratic formula is safe in such cases.
Step 3
Exam Tip
\(x^2+x-1=0\) के सरल पूर्णांक गुणनखंड नहीं मिलते, इसलिए सूत्र विधि आसान है। परीक्षा में ऐसे मामलों में द्विघात सूत्र सुरक्षित रहता है।
Login to save your score, XP, coins and progress. Login
\(x^2+x-1=0\) के मूल द्विघात सूत्र से क्या हैं?
What are the roots of \(x^2+x-1=0\) by the quadratic formula?
#quadratic
#quadratic-formula
#irrational-roots
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x=\frac{-1\pm\sqrt{5}}{2}\)
B \(x=\frac{1\pm\sqrt{5}}{2}\)
C \(x=-1\pm\sqrt{5}\)
D \(x=\frac{-1\pm\sqrt{3}}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{-1\pm\sqrt{5}}{2}\)
Step 1
Concept
Here (D=1-4(1)(-1)=5), so \(x=\frac{-1\pm\sqrt{5}}{2}\). In exams, keep the sign of (c=-1) correct.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{-1\pm\sqrt{5}}{2}\). Here (D=1-4(1)(-1)=5), so \(x=\frac{-1\pm\sqrt{5}}{2}\). In exams, keep the sign of (c=-1) correct.
Step 3
Exam Tip
यहां (D=1-4(1)(-1)=5), इसलिए \(x=\frac{-1\pm\sqrt{5}}{2}\) है। परीक्षा में (c=-1) का संकेत सही रखें।
Login to save your score, XP, coins and progress. Login
\(2x^2-3x-2=0\) में कौनसा गुणनखंड रूप सही है?
Which factorised form is correct for \(2x^2-3x-2=0\)?
#quadratic
#factorisation
#verification
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ((2x+1)(x-2)=0)
B ((2x-1)(x+2)=0)
C ((2x-2)(x+1)=0)
D ((x+2)(x-2)=0)
Explanation opens after your attempt
Correct Answer
A. ((2x+1)(x-2)=0)
Step 1
Concept
((2x+1)(x-2)=2x-2 -3x-2), so this is the correct factorised form. In exams, check the answer by expanding.
Step 2
Why this answer is correct
The correct answer is A. ((2x+1)(x-2)=0). ((2x+1)(x-2)=2x-2 -3x-2), so this is the correct factorised form. In exams, check the answer by expanding.
Step 3
Exam Tip
((2x+1)(x-2)=2x-2 -3x-2), इसलिए यह सही गुणनखंड रूप है। परीक्षा में विस्तार करके उत्तर जांचें।
Login to save your score, XP, coins and progress. Login
\(2x^2-3x-2=0\) के मूल क्या हैं?
What are the roots of \(2x^2-3x-2=0\)?
#quadratic
#roots
#factorisation
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x=2,-\frac{1}{2}\)
B \(x=-2,\frac{1}{2}\)
C (x=1,-2)
D \(x=\frac{3}{2},-1\)
Explanation opens after your attempt
Correct Answer
A. \(x=2,-\frac{1}{2}\)
Step 1
Concept
((2x+1)(x-2)=0), so \(x=-\frac{1}{2}\) and (2). In exams, change signs while writing roots.
Step 2
Why this answer is correct
The correct answer is A. \(x=2,-\frac{1}{2}\). ((2x+1)(x-2)=0), so \(x=-\frac{1}{2}\) and (2). In exams, change signs while writing roots.
Step 3
Exam Tip
((2x+1)(x-2)=0), इसलिए \(x=-\frac{1}{2}\) और (2) हैं। परीक्षा में संकेत बदलकर मूल लिखें।
Login to save your score, XP, coins and progress. Login
यदि किसी छात्र ने \(x^2=25\) से केवल (x=5) लिखा, तो सुधार क्या है?
If a student wrote only (x=5) from \(x^2=25\), what is the correction?
#quadratic
#square-root-method
#common-mistake
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(x=\pm5\) लिखना चाहिए / One should write \(x=\pm5\)
B (x=25) लिखना चाहिए / One should write (x=25)
C (x=-25) लिखना चाहिए / One should write (x=-25)
D \(x=\pm25\) लिखना चाहिए / One should write \(x=\pm25\)
Explanation opens after your attempt
Correct Answer
A. \(x=\pm5\) लिखना चाहिए / One should write \(x=\pm5\)
Step 1
Concept
From \(x^2=25\), \(x=\pm\sqrt{25}=\pm5\). In exams, both signs are necessary in the square root method.
Step 2
Why this answer is correct
The correct answer is A. \(x=\pm5\) लिखना चाहिए / One should write \(x=\pm5\). From \(x^2=25\), \(x=\pm\sqrt{25}=\pm5\). In exams, both signs are necessary in the square root method.
Step 3
Exam Tip
\(x^2=25\) से \(x=\pm\sqrt{25}=\pm5\) मिलता है। परीक्षा में वर्गमूल विधि में दोनों चिन्ह अनिवार्य हैं।
Login to save your score, XP, coins and progress. Login
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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
\(x^2-8x+15=0\) 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
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
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।
Login to save your score, XP, coins and progress. Login
