Class 10 completing-square MCQ Questions

Question 31/70 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 32/70 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 33/70 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 34/70 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 35/70 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 36/70 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 37/70 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 38/70 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 39/70 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 40/70 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 41/70 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 42/70 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 43/70 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 44/70 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 45/70 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 46/70 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 47/70 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 48/70 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 49/70 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 50/70 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 51/70 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 52/70 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 53/70 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 54/70 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 55/70 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 56/70 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 57/70 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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Question 58/70 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)?

Explanation opens after your attempt

Correct Answer

A. पूर्ण वर्ग विधिCompleting 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 59/70 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?

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 60/70 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?

Explanation opens after your attempt

Correct Answer

A. (144)

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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completing-square MCQ Questions for Class 10

Practice Questions

यदि \(x^2+4x+1=0\), तो पूर्ण वर्ग विधि से सही रूप कौनसा है?

Concept

Why this answer is correct

Exam Tip

\(3x^2-10x+3=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?

Concept

Why this answer is correct

Exam Tip

\(x^2-24x+108=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2-24x+108=0\) को पूर्ण वर्ग विधि से हल किया जाए, तो सही मध्य चरण कौनसा है?

Concept

Why this answer is correct

Exam Tip

\(x^2-6x+18=0\) में पूर्ण वर्ग बनाने पर कौनसा रूप बनेगा?

Concept

Why this answer is correct

Exam Tip

\(x^2+8x-33=0\) के मूल क्या हैं?

Concept

Why this answer is correct

Exam Tip

\(x^2+8x-33=0\) को पूर्ण वर्ग विधि से हल करने में सही चरण कौनसा है?

Concept

Why this answer is correct

Exam Tip

\(x^2-18x+45=0\) के मूल क्या हैं?

Concept

Why this answer is correct

Exam Tip

\(x^2-18x+45=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?

Concept

Why this answer is correct

Exam Tip

\(x^2-10x+24=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?

Concept

Why this answer is correct

Exam Tip

\(x^2-6x-7=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2-6x-7=0\) को पूर्ण वर्ग विधि से हल किया जाए, तो सही मध्य चरण कौनसा है?

Concept

Why this answer is correct

Exam Tip

\(x^2-4x+13=0\) में पूर्ण वर्ग बनाने पर कौनसा रूप बनेगा?

Concept

Why this answer is correct

Exam Tip

\(x^2+2x-24=0\) के मूल क्या हैं?

Concept

Why this answer is correct

Exam Tip

\(x^2+2x-24=0\) को पूर्ण वर्ग विधि से हल करने में सही चरण कौनसा है?

Concept

Why this answer is correct

Exam Tip

\(x^2-16x+28=0\) के मूल क्या हैं?

Concept

Why this answer is correct

Exam Tip

\(x^2-16x+28=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?

Concept

Why this answer is correct

Exam Tip

\(x^2-8x+12=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?

Concept

Why this answer is correct

Exam Tip

\(x^2-8x+15=0\) के मूल पूर्ण वर्ग विधि से क्या मिलेंगे?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2-8x+15=0\) को पूर्ण वर्ग विधि से हल किया जाए, तो सही मध्य चरण कौनसा है?

Concept

किस विधि में समीकरण को पहले ((x+p)²=q) जैसे रूप में बदला जाता है?