Search: other root

Question Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

यदि \(x^2-25x+q=0\) का एक मूल (10) है, तो दूसरा मूल क्या होगा?

If one root of \(x^2-25x+q=0\) is (10), what will be the other root?

Explanation opens after your attempt

Correct Answer

A. (15)

Step 1

Concept

The sum of roots is (25), so the other root is (25-10=15). In exams, use the sum when one root is given.

Step 2

Why this answer is correct

The correct answer is A. (15). The sum of roots is (25), so the other root is (25-10=15). In exams, use the sum when one root is given.

Step 3

Exam Tip

मूलों का योग (25) है, इसलिए दूसरा मूल (25-10=15) होगा। परीक्षा में एक मूल दिया हो तो योग का प्रयोग करें।

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Question Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

यदि \(x^2-23x+q=0\) का एक मूल (9) है, तो दूसरा मूल क्या होगा?

If one root of \(x^2-23x+q=0\) is (9), what will be the other root?

Explanation opens after your attempt

Correct Answer

A. (14)

Step 1

Concept

The sum of roots is (23), so the other root is (23-9=14). In exams, use the sum when one root is given.

Step 2

Why this answer is correct

The correct answer is A. (14). The sum of roots is (23), so the other root is (23-9=14). In exams, use the sum when one root is given.

Step 3

Exam Tip

मूलों का योग (23) है, इसलिए दूसरा मूल (23-9=14) होगा। परीक्षा में एक मूल दिया हो तो योग का प्रयोग करें।

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Question Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

यदि \(x^2-21x+q=0\) का एक मूल (8) है, तो दूसरा मूल क्या होगा?

If one root of \(x^2-21x+q=0\) is (8), what will be the other root?

Explanation opens after your attempt

Correct Answer

A. (13)

Step 1

Concept

The sum of roots is (21), so the other root is (21-8=13). In exams, use the sum when one root is given.

Step 2

Why this answer is correct

The correct answer is A. (13). The sum of roots is (21), so the other root is (21-8=13). In exams, use the sum when one root is given.

Step 3

Exam Tip

मूलों का योग (21) है, इसलिए दूसरा मूल (21-8=13) होगा। परीक्षा में एक मूल दिया हो तो योग का उपयोग करें।

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Question Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

यदि \(x^2-15x+q=0\) का एक मूल (6) है, तो दूसरा मूल क्या होगा?

If one root of \(x^2-15x+q=0\) is (6), what will be the other root?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

The sum of roots is (15), so the other root is (15-6=9). In exams, use the sum when one root is given.

Step 2

Why this answer is correct

The correct answer is A. (9). The sum of roots is (15), so the other root is (15-6=9). In exams, use the sum when one root is given.

Step 3

Exam Tip

मूलों का योग (15) है, इसलिए दूसरा मूल (15-6=9) होगा। परीक्षा में एक मूल दिया हो तो योग का प्रयोग करें।

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Question Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

यदि \(x^2-9x+q=0\) का एक मूल (4) है, तो दूसरा मूल क्या होगा?

If one root of \(x^2-9x+q=0\) is (4), what will be the other root?

Explanation opens after your attempt

Correct Answer

A. (5)

Step 1

Concept

The sum of roots is (9), so the other root is (9-4=5). In exams, use the sum when one root is given.

Step 2

Why this answer is correct

The correct answer is A. (5). The sum of roots is (9), so the other root is (9-4=5). In exams, use the sum when one root is given.

Step 3

Exam Tip

मूलों का योग (9) है, इसलिए दूसरा मूल (9-4=5) होगा। परीक्षा में एक मूल दिया हो तो योग का प्रयोग करें।

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Question Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

यदि \(x^2-5x+q=0\) का एक मूल (2) है, तो दूसरा मूल क्या होगा?

If one root of \(x^2-5x+q=0\) is (2), what will be the other root?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

The sum of roots is (5), so the other root is (5-2=3). In exams, use sum or product when one root is given.

Step 2

Why this answer is correct

The correct answer is A. (3). The sum of roots is (5), so the other root is (5-2=3). In exams, use sum or product when one root is given.

Step 3

Exam Tip

मूलों का योग (5) है, इसलिए दूसरा मूल (5-2=3) होगा। परीक्षा में एक मूल दिया हो तो योग या गुणनफल का प्रयोग करें।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

यदि (4x^-2-(4h+1)x+h=0) की एक जड़ \(\frac{1}{4}\) है, तो दूसरी जड़ क्या है?

If one root of (4x^-2-(4h+1)x+h=0) is \(\frac{1}{4}\), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (h)

Step 1

Concept

The product of roots is \(\frac{h}{4}\). Since one root is \(\frac{1}{4}\), the other root is (h).

Step 2

Why this answer is correct

The correct answer is A. (h). The product of roots is \(\frac{h}{4}\). Since one root is \(\frac{1}{4}\), the other root is (h).

Step 3

Exam Tip

जड़ों का गुणनफल \(\frac{h}{4}\) है। एक जड़ \(\frac{1}{4}\) है, इसलिए दूसरी जड़ (h) होगी।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

यदि (x^-2-(m+9)x+9m=0) की एक जड़ (9) है, तो दूसरी जड़ क्या है?

If one root of (x^-2-(m+9)x+9m=0) is (9), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (m)

Step 1

Concept

The product of roots is (9m). Since one root is (9), the other root is \(\frac{9m}{9}=m\).

Step 2

Why this answer is correct

The correct answer is A. (m). The product of roots is (9m). Since one root is (9), the other root is \(\frac{9m}{9}=m\).

Step 3

Exam Tip

जड़ों का गुणनफल (9m) है। एक जड़ (9) है, इसलिए दूसरी जड़ \(\frac{9m}{9}=m\) होगी।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (2x^-2-(3p+2)x+p(p+2)=0) की एक जड़ (p) है, तो दूसरी जड़ क्या होगी?

If one root of (2x^-2-(3p+2)x+p(p+2)=0) is (p), what will be the other root?

Explanation opens after your attempt

Correct Answer

A. \(\frac{p+2}{2}\)

Step 1

Concept

The product of roots is (\frac{p(p+2)}{2}). If one root is (p), the other root is \(\frac{p+2}{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{p+2}{2}\). The product of roots is (\frac{p(p+2)}{2}). If one root is (p), the other root is \(\frac{p+2}{2}\).

Step 3

Exam Tip

जड़ों का गुणनफल (\frac{p(p+2)}{2}) है। एक जड़ (p) होने पर दूसरी जड़ \(\frac{p+2}{2}\) होगी।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि (3x^-2-(3h+1)x+h=0) की एक जड़ \(\frac{1}{3}\) है, तो दूसरी जड़ क्या है?

If one root of (3x^-2-(3h+1)x+h=0) is \(\frac{1}{3}\), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (h)

Step 1

Concept

The product of roots is \(\frac{h}{3}\). Since one root is \(\frac{1}{3}\), the other root is (h).

Step 2

Why this answer is correct

The correct answer is A. (h). The product of roots is \(\frac{h}{3}\). Since one root is \(\frac{1}{3}\), the other root is (h).

Step 3

Exam Tip

जड़ों का गुणनफल \(\frac{h}{3}\) है। एक जड़ \(\frac{1}{3}\) है, इसलिए दूसरी जड़ (h) होगी।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि (2x^-2-(h+1)x+h=0) की जड़ों में से एक हमेशा \(\frac{1}{2}\) है, तो दूसरी जड़ क्या होगी?

If one root of (2x^-2-(h+1)x+h=0) is always \(\frac{1}{2}\), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (h)

Step 1

Concept

The product is \(\frac{h}{2}\). Since one root is \(\frac{1}{2}\), the other root is \(\frac{h}{2}\div\frac{1}{2}=h\).

Step 2

Why this answer is correct

The correct answer is A. (h). The product is \(\frac{h}{2}\). Since one root is \(\frac{1}{2}\), the other root is \(\frac{h}{2}\div\frac{1}{2}=h\).

Step 3

Exam Tip

गुणनफल \(\frac{h}{2}\) है। एक जड़ \(\frac{1}{2}\) है, इसलिए दूसरी जड़ \(\frac{h}{2}\div\frac{1}{2}=h\) होगी।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि (x^-2-(m+2)x+3m=0) की एक जड़ (3) है, तो दूसरी जड़ क्या है?

If one root of (x^-2-(m+2)x+3m=0) is (3), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (m)

Step 1

Concept

Putting (x=3) makes the equation true for every (m). The product is (3m) and one root is (3), so the other root is (m).

Step 2

Why this answer is correct

The correct answer is A. (m). Putting (x=3) makes the equation true for every (m). The product is (3m) and one root is (3), so the other root is (m).

Step 3

Exam Tip

(x=3) रखने पर समीकरण हर (m) के लिए सही हो जाता है। गुणनफल (3m) है और एक जड़ (3), इसलिए दूसरी जड़ (m) है।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि (x^-2-(m^-2)x+m^-6=0) की एक जड़ (3) है, तो दूसरी जड़ क्या होगी?

If one root of (x^-2-(m^-2)x+m^-6=0) is (3), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

Putting (x=3) gives (9-3(m^-2)+m^-6=0), so \(m=\frac{9}{2}\). The product is \(-\frac{3}{2}\), so the other root is \(-\frac{1}{2}\); hence no option is correct.

Step 2

Why this answer is correct

The correct answer is A. (1). Putting (x=3) gives (9-3(m^-2)+m^-6=0), so \(m=\frac{9}{2}\). The product is \(-\frac{3}{2}\), so the other root is \(-\frac{1}{2}\); hence no option is correct.

Step 3

Exam Tip

(x=3) रखने पर (9-3(m^-2)+m^-6=0), इसलिए \(m=\frac{9}{2}\)। गुणनफल \(m-6=-\frac{3}{2}\) है, अतः दूसरी जड़ \(-\frac{1}{2}\) होगी, इसलिए कोई विकल्प सही नहीं है।

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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

यदि \(x^2+ax+12=0\) की एक जड़ दूसरी जड़ से (3) अधिक है, तो (a) के संभव मान क्या हैं?

If one root of \(x^2+ax+12=0\) is (3) more than the other root, what are the possible values of (a)?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{57}\) और \(-\sqrt{57}\)\(\sqrt{57}\) and \(-\sqrt{57}\)

Step 1

Concept

Let the roots be (r) and (r+3). Then (r(r+3)=12), giving the sum as \(\pm\sqrt{57}\), so \(a=\mp\sqrt{57}\).

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{57}\) और \(-\sqrt{57}\) / \(\sqrt{57}\) and \(-\sqrt{57}\). Let the roots be (r) and (r+3). Then (r(r+3)=12), giving the sum as \(\pm\sqrt{57}\), so \(a=\mp\sqrt{57}\).

Step 3

Exam Tip

जड़ें (r) और (r+3) मानने पर (r(r+3)=12) मिलता है। इससे जड़ों का योग \(\pm\sqrt{57}\) होता है, इसलिए \(a=\mp\sqrt{57}\)।

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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

यदि (x^-2+(k-3)x+k=0) की एक जड़ दूसरी जड़ की दुगुनी है, तो (k) का मान क्या होगा?

If one root of (x^-2+(k-3)x+k=0) is twice the other root, what is the value of (k)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{21+3\sqrt{33}}{4}\) या \(\frac{21-3\sqrt{33}}{4}\)\(\frac{21+3\sqrt{33}}{4}\) or \(\frac{21-3\sqrt{33}}{4}\)

Step 1

Concept

Taking the roots as (r) and (2r), we get (3r=3-k) and \(2r^2=k\). Solving \(2k^2-21k+18=0\) gives the two listed values.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{21+3\sqrt{33}}{4}\) या \(\frac{21-3\sqrt{33}}{4}\) / \(\frac{21+3\sqrt{33}}{4}\) or \(\frac{21-3\sqrt{33}}{4}\). Taking the roots as (r) and (2r), we get (3r=3-k) and \(2r^2=k\). Solving \(2k^2-21k+18=0\) gives the two listed values.

Step 3

Exam Tip

जड़ें (r) और (2r) मानने पर (3r=3-k) और \(2r^2=k\) मिलता है। हल करने पर \(2k^2-21k+18=0\), इसलिए दिए गए दोनों मान मिलते हैं।

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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि \(x^2+ax+a=0\) का एक मूल (2) है तो दूसरा मूल क्या होगा?

If one root of \(x^2+ax+a=0\) is (2), what will be the other root?

Explanation opens after your attempt

Correct Answer

A. \(-\frac{2}{3}\)

Step 1

Concept

Putting (x=2) gives (4+3a=0), so \(a=-\frac{4}{3}\). The product is (a), so the other root is \(-\frac{2}{3}\).

Step 2

Why this answer is correct

The correct answer is A. \(-\frac{2}{3}\). Putting (x=2) gives (4+3a=0), so \(a=-\frac{4}{3}\). The product is (a), so the other root is \(-\frac{2}{3}\).

Step 3

Exam Tip

(x=2) रखने पर (4+3a=0) से \(a=-\frac{4}{3}\) है। गुणनफल (a) है इसलिए दूसरा मूल \(-\frac{2}{3}\) होगा।

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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि \(x^2+ax+a=0\) का एक मूल (1) है तो दूसरा मूल क्या होगा?

If one root of \(x^2+ax+a=0\) is (1), what will be the other root?

Explanation opens after your attempt

Correct Answer

A. \(-\frac{1}{2}\)

Step 1

Concept

Putting (x=1) gives (1+2a=0), so \(a=-\frac{1}{2}\). The product is (a), so the other root is \(-\frac{1}{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(-\frac{1}{2}\). Putting (x=1) gives (1+2a=0), so \(a=-\frac{1}{2}\). The product is (a), so the other root is \(-\frac{1}{2}\).

Step 3

Exam Tip

(x=1) रखने पर (1+2a=0) से \(a=-\frac{1}{2}\) है। गुणनफल (a) है इसलिए दूसरा मूल \(-\frac{1}{2}\) होगा।

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Question Medium Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

समीकरण \(x^2-17x+70=0\) का एक मूल (7) है तो दूसरा मूल क्या है?

If one root of \(x^2-17x+70=0\) is (7), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (10)

Step 1

Concept

The product of roots is (70) and one root is (7). The other root is \(\frac{70}{7}=10\).

Step 2

Why this answer is correct

The correct answer is A. (10). The product of roots is (70) and one root is (7). The other root is \(\frac{70}{7}=10\).

Step 3

Exam Tip

मूलों का गुणनफल (70) है और एक मूल (7) है। दूसरा मूल \(\frac{70}{7}=10\) होगा।

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Question Medium Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-15x+54=0\) का एक मूल (6) है तो दूसरा मूल क्या है?

If one root of \(x^2-15x+54=0\) is (6), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

The product of roots is (54) and one root is (6). Therefore the other root is \(\frac{54}{6}=9\).

Step 2

Why this answer is correct

The correct answer is A. (9). The product of roots is (54) and one root is (6). Therefore the other root is \(\frac{54}{6}=9\).

Step 3

Exam Tip

मूलों का गुणनफल (54) है और एक मूल (6) है। इसलिए दूसरा मूल \(\frac{54}{6}=9\) है।

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Question Medium Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

समीकरण \(x^2-13x+40=0\) का एक मूल (5) है तो दूसरा मूल क्या है?

If one root of \(x^2-13x+40=0\) is (5), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

The product of roots is (40) and one root is (5). Therefore the other root is \(\frac{40}{5}=8\).

Step 2

Why this answer is correct

The correct answer is A. (8). The product of roots is (40) and one root is (5). Therefore the other root is \(\frac{40}{5}=8\).

Step 3

Exam Tip

मूलों का गुणनफल (40) है और एक मूल (5) है। इसलिए दूसरा मूल \(\frac{40}{5}=8\) है।

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Question Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

यदि मूलों का योग (12) है और एक मूल (5) है तो दूसरा मूल क्या है?

If the sum of roots is (12) and one root is (5), what is the other root?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

The other root is (12-5=7). Subtract the given root from the sum.

Step 2

Why this answer is correct

The correct answer is B. (7). The other root is (12-5=7). Subtract the given root from the sum.

Step 3

Exam Tip

दूसरा मूल (12-5=7) है। योग में से दिया हुआ मूल घटाएं।

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Question Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

यदि एक मूल (6) है और मूलों का गुणनफल (48) है तो दूसरा मूल क्या होगा?

If one root is (6) and the product of roots is (48), what is the other root?

Explanation opens after your attempt

Correct Answer

B. (8)

Step 1

Concept

The other root is \(\frac{48}{6}=8\). Divide the product by the given root.

Step 2

Why this answer is correct

The correct answer is B. (8). The other root is \(\frac{48}{6}=8\). Divide the product by the given root.

Step 3

Exam Tip

दूसरा मूल \(\frac{48}{6}=8\) होगा। गुणनफल को दिए हुए मूल से भाग करें।

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Question Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

समीकरण \(x^2-11x+30=0\) का एक मूल (5) है तो दूसरा मूल क्या है?

If one root of \(x^2-11x+30=0\) is (5), what is the other root?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

(x^-2-11x+30=(x-5)(x-6)). Therefore the other root is (6).

Step 2

Why this answer is correct

The correct answer is B. (6). (x^-2-11x+30=(x-5)(x-6)). Therefore the other root is (6).

Step 3

Exam Tip

(x^-2-11x+30=(x-5)(x-6)) है। इसलिए दूसरा मूल (6) है।

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Question Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि मूलों का योग (8) है और एक मूल (3) है तो दूसरा मूल क्या है?

If the sum of roots is (8) and one root is (3), what is the other root?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

The other root is (8-3=5). Subtract the given root from the sum.

Step 2

Why this answer is correct

The correct answer is B. (5). The other root is (8-3=5). Subtract the given root from the sum.

Step 3

Exam Tip

दूसरा मूल (8-3=5) है। योग में से दिया हुआ मूल घटाएं।

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Question Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि एक मूल (5) है और मूलों का गुणनफल (35) है तो दूसरा मूल क्या होगा?

If one root is (5) and the product of roots is (35), what is the other root?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

The other root is \(\frac{35}{5}=7\). Divide the product by the given root.

Step 2

Why this answer is correct

The correct answer is B. (7). The other root is \(\frac{35}{5}=7\). Divide the product by the given root.

Step 3

Exam Tip

दूसरा मूल \(\frac{35}{5}=7\) होगा। गुणनफल में दिए हुए मूल से भाग करें।

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Question Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

समीकरण \(x^2-9x+18=0\) का एक मूल (3) है तो दूसरा मूल क्या है?

If one root of \(x^2-9x+18=0\) is (3), what is the other root?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

(x^-2-9x+18=(x-3)(x-6)). Therefore the other root is (6).

Step 2

Why this answer is correct

The correct answer is B. (6). (x^-2-9x+18=(x-3)(x-6)). Therefore the other root is (6).

Step 3

Exam Tip

(x^-2-9x+18=(x-3)(x-6)) है। इसलिए दूसरा मूल (6) है।

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Question Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि मूलों का योग (5) है और एक मूल (2) है तो दूसरा मूल क्या है?

If the sum of roots is (5) and one root is (2) then what is the other root?

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

The other root is (5-2=3). Subtract the given root from the sum.

Step 2

Why this answer is correct

The correct answer is B. (3). The other root is (5-2=3). Subtract the given root from the sum.

Step 3

Exam Tip

दूसरा मूल (5-2=3) है। योग में से दिए हुए मूल को घटाएं।

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Question Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि एक मूल (3) है और मूलों का गुणनफल (12) है तो दूसरा मूल क्या होगा?

If one root is (3) and the product of roots is (12) then what is the other root?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

The other root is \(\frac{12}{3}=4\). In product questions divide by the given root.

Step 2

Why this answer is correct

The correct answer is B. (4). The other root is \(\frac{12}{3}=4\). In product questions divide by the given root.

Step 3

Exam Tip

दूसरा मूल \(\frac{12}{3}=4\) होगा। गुणनफल वाले प्रश्न में दिए मूल से भाग दें।

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Question Easy Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

समीकरण \(x^2-6x+8=0\) का एक मूल (4) है तो दूसरा मूल क्या है?

If one root of \(x^2-6x+8=0\) is (4) then what is the other root?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

(x^-2-6x+8=(x-4)(x-2)) so the other root is (2). Use the given root to find the other factor.

Step 2

Why this answer is correct

The correct answer is B. (2). (x^-2-6x+8=(x-4)(x-2)) so the other root is (2). Use the given root to find the other factor.

Step 3

Exam Tip

(x^-2-6x+8=(x-4)(x-2)) इसलिए दूसरा मूल (2) है। दिए गए एक मूल से दूसरा गुणनखंड खोजें।

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Question Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि (x^-2-(m+7)x+7m=0) का एक मूल (7) है, तो दूसरा मूल क्या है?

If one root of (x^-2-(m+7)x+7m=0) is (7), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (m)

Step 1

Concept

The product of roots is (7m) and one root is (7). Hence the other root is \(\frac{7m}{7}=m\).

Step 2

Why this answer is correct

The correct answer is A. (m). The product of roots is (7m) and one root is (7). Hence the other root is \(\frac{7m}{7}=m\).

Step 3

Exam Tip

मूलों का गुणनफल (7m) है और एक मूल (7) है। इसलिए दूसरा मूल \(\frac{7m}{7}=m\) है।

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Question Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2+ax+54=0\) का एक मूल (6) है, तो दूसरा मूल और (a) कौन-से हैं?

If one root of \(x^2+ax+54=0\) is (6), what are the other root and (a)?

Explanation opens after your attempt

Correct Answer

A. दूसरा मूल (9), (a=-15)other root (9), (a=-15)

Step 1

Concept

The product of roots is (54), so the other root is (9). The sum is (15), and (-a=15), so (a=-15).

Step 2

Why this answer is correct

The correct answer is A. दूसरा मूल (9), (a=-15) / other root (9), (a=-15). The product of roots is (54), so the other root is (9). The sum is (15), and (-a=15), so (a=-15).

Step 3

Exam Tip

मूलों का गुणनफल (54) है, इसलिए दूसरा मूल (9) होगा। योग (15) है और (-a=15), इसलिए (a=-15)।

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Question Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि (x^-2-(m+6)x+6m=0) का एक मूल (6) है, तो दूसरा मूल क्या है?

If one root of (x^-2-(m+6)x+6m=0) is (6), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (m)

Step 1

Concept

The product of roots is (6m) and one root is (6). Hence the other root is \(\frac{6m}{6}=m\).

Step 2

Why this answer is correct

The correct answer is A. (m). The product of roots is (6m) and one root is (6). Hence the other root is \(\frac{6m}{6}=m\).

Step 3

Exam Tip

मूलों का गुणनफल (6m) है और एक मूल (6) है। इसलिए दूसरा मूल \(\frac{6m}{6}=m\) है।

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Question Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि \(x^2+ax+40=0\) का एक मूल (5) है, तो दूसरा मूल और (a) कौन-से हैं?

If one root of \(x^2+ax+40=0\) is (5), what are the other root and (a)?

Explanation opens after your attempt

Correct Answer

A. दूसरा मूल (8), (a=-13)other root (8), (a=-13)

Step 1

Concept

The product of roots is (40), so the other root is (8). The sum is (13), and (-a=13), so (a=-13).

Step 2

Why this answer is correct

The correct answer is A. दूसरा मूल (8), (a=-13) / other root (8), (a=-13). The product of roots is (40), so the other root is (8). The sum is (13), and (-a=13), so (a=-13).

Step 3

Exam Tip

मूलों का गुणनफल (40) है, इसलिए दूसरा मूल (8) होगा। योग (13) है और (-a=13), इसलिए (a=-13)।

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Question Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

यदि (x^-2-(m+5)x+5m=0) का एक मूल (5) है, तो दूसरा मूल क्या है?

If one root of (x^-2-(m+5)x+5m=0) is (5), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (m)

Step 1

Concept

The product of roots is (5m) and one root is (5). Hence the other root is \(\frac{5m}{5}=m\).

Step 2

Why this answer is correct

The correct answer is A. (m). The product of roots is (5m) and one root is (5). Hence the other root is \(\frac{5m}{5}=m\).

Step 3

Exam Tip

मूलों का गुणनफल (5m) है और एक मूल (5) है। इसलिए दूसरा मूल \(\frac{5m}{5}=m\) है।

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Question Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

यदि \(x^2+ax+24=0\) का एक मूल (4) है, तो दूसरा मूल और (a) कौन-से हैं?

If one root of \(x^2+ax+24=0\) is (4), what are the other root and (a)?

Explanation opens after your attempt

Correct Answer

A. दूसरा मूल (6), (a=-10)other root (6), (a=-10)

Step 1

Concept

The product of roots is (24), so the other root is (6). The sum is (10), and (-a=10), so (a=-10).

Step 2

Why this answer is correct

The correct answer is A. दूसरा मूल (6), (a=-10) / other root (6), (a=-10). The product of roots is (24), so the other root is (6). The sum is (10), and (-a=10), so (a=-10).

Step 3

Exam Tip

मूलों का गुणनफल (24) है, इसलिए दूसरा मूल (6) होगा। योग (10) है और (-a=10), इसलिए (a=-10)।

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Question Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

किस समीकरण में (x=0) एक मूल है और दूसरा मूल ऋणात्मक है?

In which equation is (x=0) one root and the other root negative?

Explanation opens after your attempt

Correct Answer

A. \(x^2+7x=0\)

Step 1

Concept

(x^-2+7x=x(x+7)), so the roots are (0) and (-7). The other root is negative.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+7x=0\). (x^-2+7x=x(x+7)), so the roots are (0) and (-7). The other root is negative.

Step 3

Exam Tip

(x^-2+7x=x(x+7)), इसलिए मूल (0) और (-7) हैं। दूसरा मूल ऋणात्मक है।

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Question Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि (x^-2-(m+4)x+4m=0) का एक मूल (4) है, तो दूसरा मूल क्या है?

If one root of (x^-2-(m+4)x+4m=0) is (4), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (m)

Step 1

Concept

The product of roots is (4m) and one root is (4). Hence the other root is \(\frac{4m}{4}=m\).

Step 2

Why this answer is correct

The correct answer is A. (m). The product of roots is (4m) and one root is (4). Hence the other root is \(\frac{4m}{4}=m\).

Step 3

Exam Tip

गुणनफल (4m) है और एक मूल (4) है। इसलिए दूसरा मूल \(\frac{4m}{4}=m\) है।

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Question Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2+ax+18=0\) का एक मूल (2) है, तो दूसरा मूल और (a) कौन-से हैं?

If one root of \(x^2+ax+18=0\) is (2), what are the other root and (a)?

Explanation opens after your attempt

Correct Answer

A. दूसरा मूल (9), (a=-11)other root (9), (a=-11)

Step 1

Concept

The product of roots is (18), so the other root is (9). The sum is (11), and (-a=11), so (a=-11).

Step 2

Why this answer is correct

The correct answer is A. दूसरा मूल (9), (a=-11) / other root (9), (a=-11). The product of roots is (18), so the other root is (9). The sum is (11), and (-a=11), so (a=-11).

Step 3

Exam Tip

मूलों का गुणनफल (18) है, इसलिए दूसरा मूल (9) होगा। योग (11) है और (-a=11), इसलिए (a=-11)।

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Question Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

किस समीकरण में (x=0) एक मूल है और दूसरा मूल धनात्मक है?

In which equation is (x=0) one root and the other root positive?

Explanation opens after your attempt

Correct Answer

A. \(x^2-6x=0\)

Step 1

Concept

(x^-2-6x=x(x-6)), so the roots are (0) and (6). The other root is positive.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-6x=0\). (x^-2-6x=x(x-6)), so the roots are (0) and (6). The other root is positive.

Step 3

Exam Tip

(x^-2-6x=x(x-6)), इसलिए मूल (0) और (6) हैं। दूसरा मूल धनात्मक है।

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Question Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि (x^-2-(m+2)x+2m=0) का एक मूल (2) है, तो दूसरा मूल क्या है?

If one root of (x^-2-(m+2)x+2m=0) is (2), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (m)

Step 1

Concept

The product of roots is (2m) and one root is (2). Hence the other root is \(\frac{2m}{2}=m\).

Step 2

Why this answer is correct

The correct answer is A. (m). The product of roots is (2m) and one root is (2). Hence the other root is \(\frac{2m}{2}=m\).

Step 3

Exam Tip

गुणनफल (2m) है और एक मूल (2) है। इसलिए दूसरा मूल \(\frac{2m}{2}=m\) है।

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Question Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि \(x^2+ax+12=0\) का एक मूल (3) है, तो दूसरा मूल और (a) कौन-से हैं?

If one root of \(x^2+ax+12=0\) is (3), what are the other root and (a)?

Explanation opens after your attempt

Correct Answer

A. दूसरा मूल (4), (a=-7)other root (4), (a=-7)

Step 1

Concept

The product of roots is (12), so the other root is (4). The sum is (7), and (-a=7), so (a=-7).

Step 2

Why this answer is correct

The correct answer is A. दूसरा मूल (4), (a=-7) / other root (4), (a=-7). The product of roots is (12), so the other root is (4). The sum is (7), and (-a=7), so (a=-7).

Step 3

Exam Tip

मूलों का गुणनफल (12) है, इसलिए दूसरा मूल (4) होगा। योग (7) है और (-a=7), इसलिए (a=-7)।

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Question Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

यदि \(x^2-25x+q=0\) का एक मूल (10) है, तो (q) का मान क्या होगा?

If one root of \(x^2-25x+q=0\) is (10), what is the value of (q)?

Explanation opens after your attempt

Correct Answer

A. (150)

Step 1

Concept

The other root is (15), so \(q=10\times15=150\). In exams, when (a=1), the constant term is the product of roots.

Step 2

Why this answer is correct

The correct answer is A. (150). The other root is (15), so \(q=10\times15=150\). In exams, when (a=1), the constant term is the product of roots.

Step 3

Exam Tip

दूसरा मूल (15) है, इसलिए \(q=10\times15=150\) होगा। परीक्षा में (a=1) हो तो स्थिर पद मूलों का गुणनफल होता है।

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Question Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

यदि \(x^2-23x+q=0\) का एक मूल (9) है, तो (q) का मान क्या होगा?

If one root of \(x^2-23x+q=0\) is (9), what is the value of (q)?

Explanation opens after your attempt

Correct Answer

A. (126)

Step 1

Concept

The other root is (14), so \(q=9\times14=126\). In exams, when (a=1), the constant term is the product of roots.

Step 2

Why this answer is correct

The correct answer is A. (126). The other root is (14), so \(q=9\times14=126\). In exams, when (a=1), the constant term is the product of roots.

Step 3

Exam Tip

दूसरा मूल (14) है, इसलिए \(q=9\times14=126\) होगा। परीक्षा में (a=1) हो तो स्थिर पद मूलों का गुणनफल होता है।

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Question Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

यदि \(x^2-21x+q=0\) का एक मूल (8) है, तो (q) का मान क्या होगा?

If one root of \(x^2-21x+q=0\) is (8), what is the value of (q)?

Explanation opens after your attempt

Correct Answer

A. (104)

Step 1

Concept

The other root is (13), so \(q=8\times13=104\). In exams, when (a=1), the constant term is the product of roots.

Step 2

Why this answer is correct

The correct answer is A. (104). The other root is (13), so \(q=8\times13=104\). In exams, when (a=1), the constant term is the product of roots.

Step 3

Exam Tip

दूसरा मूल (13) है, इसलिए \(q=8\times13=104\) होगा। परीक्षा में (a=1) हो तो स्थिर पद मूलों का गुणनफल होता है।

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Question Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

यदि \(x^2-15x+q=0\) का एक मूल (6) है, तो (q) का मान क्या होगा?

If one root of \(x^2-15x+q=0\) is (6), what is the value of (q)?

Explanation opens after your attempt

Correct Answer

A. (54)

Step 1

Concept

The other root is (9), so \(q=6\times9=54\). In exams, when (a=1), (c) equals the product of roots.

Step 2

Why this answer is correct

The correct answer is A. (54). The other root is (9), so \(q=6\times9=54\). In exams, when (a=1), (c) equals the product of roots.

Step 3

Exam Tip

दूसरा मूल (9) है, इसलिए \(q=6\times9=54\) होगा। परीक्षा में (a=1) हो तो (c) मूलों के गुणनफल के बराबर होता है।

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Question Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

यदि \(x^2-9x+q=0\) का एक मूल (4) है, तो (q) का मान क्या होगा?

If one root of \(x^2-9x+q=0\) is (4), what is the value of (q)?

Explanation opens after your attempt

Correct Answer

A. (20)

Step 1

Concept

The other root is (5), so \(q=4\times5=20\). In exams, (c) equals the product of roots when (a=1).

Step 2

Why this answer is correct

The correct answer is A. (20). The other root is (5), so \(q=4\times5=20\). In exams, (c) equals the product of roots when (a=1).

Step 3

Exam Tip

दूसरा मूल (5) है, इसलिए \(q=4\times5=20\) होगा। परीक्षा में (c) मूलों के गुणनफल के बराबर होता है जब (a=1)।

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Question Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

यदि \(x^2-5x+q=0\) का एक मूल (2) है, तो (q) का मान क्या होगा?

If one root of \(x^2-5x+q=0\) is (2), what is the value of (q)?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

The other root is (3), so \(q=2\times3=6\). In exams, connect (c) with product of roots.

Step 2

Why this answer is correct

The correct answer is A. (6). The other root is (3), so \(q=2\times3=6\). In exams, connect (c) with product of roots.

Step 3

Exam Tip

दूसरा मूल (3) है, इसलिए \(q=2\times3=6\) होगा। परीक्षा में (c) को मूलों के गुणनफल से जोड़ें।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

(x^-2-(a+8)x+8a=0) के बारे में कौन-सा कथन हमेशा सही है?

Which statement is always correct about (x^-2-(a+8)x+8a=0)?

Explanation opens after your attempt

Correct Answer

A. (8) हमेशा एक जड़ है(8) is always one root

Step 1

Concept

Putting (x=8) gives (64-8(a+8)+8a=0). Hence (8) is always one root and the other root is (a).

Step 2

Why this answer is correct

The correct answer is A. (8) हमेशा एक जड़ है / (8) is always one root. Putting (x=8) gives (64-8(a+8)+8a=0). Hence (8) is always one root and the other root is (a).

Step 3

Exam Tip

(x=8) रखने पर (64-8(a+8)+8a=0) मिलता है। इसलिए (8) हमेशा एक जड़ है और दूसरी जड़ (a) है।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

(x^-2-(a+6)x+6a=0) के लिए कौन-सा कथन हमेशा सत्य है?

Which statement is always true for (x^-2-(a+6)x+6a=0)?

Explanation opens after your attempt

Correct Answer

B. (6) हमेशा जड़ है(6) is always a root

Step 1

Concept

Putting (x=6) gives (36-6(a+6)+6a=0). Hence (6) is always one root and the other root is (a).

Step 2

Why this answer is correct

The correct answer is B. (6) हमेशा जड़ है / (6) is always a root. Putting (x=6) gives (36-6(a+6)+6a=0). Hence (6) is always one root and the other root is (a).

Step 3

Exam Tip

(x=6) रखने पर (36-6(a+6)+6a=0) मिलता है। इसलिए (6) हमेशा एक जड़ है और दूसरी जड़ (a) है।

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Question Expert Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

(x^-2-(a+4)x+4a=0) के लिए कौन-सा कथन हमेशा सत्य है?

Which statement is always true for (x^-2-(a+4)x+4a=0)?

Explanation opens after your attempt

Correct Answer

A. (4) हमेशा एक जड़ है(4) is always a root

Step 1

Concept

Putting (x=4) gives (16-4(a+4)+4a=0). Hence (4) is always one root and the other root is (a).

Step 2

Why this answer is correct

The correct answer is A. (4) हमेशा एक जड़ है / (4) is always a root. Putting (x=4) gives (16-4(a+4)+4a=0). Hence (4) is always one root and the other root is (a).

Step 3

Exam Tip

(x=4) रखने पर (16-4(a+4)+4a=0) मिलता है। अतः (4) हमेशा एक जड़ है और दूसरी जड़ (a) होती है।

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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33

(x^-2-(a+3)x+3a=0) के बारे में कौन-सा कथन हमेशा सही है?

Which statement is always true about (x^-2-(a+3)x+3a=0)?

Explanation opens after your attempt

Correct Answer

A. (3) हमेशा एक जड़ है(3) is always a root

Step 1

Concept

Putting (x=3) gives (9-3(a+3)+3a=0). Hence (3) is always one root, and the other root is (a).

Step 2

Why this answer is correct

The correct answer is A. (3) हमेशा एक जड़ है / (3) is always a root. Putting (x=3) gives (9-3(a+3)+3a=0). Hence (3) is always one root, and the other root is (a).

Step 3

Exam Tip

(x=3) रखने पर (9-3(a+3)+3a=0) मिलता है। इसलिए (3) हमेशा एक जड़ है और दूसरी जड़ (a) होती है।

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यदि \(x^2-25x+q=0\) का एक मूल (10) है, तो दूसरा मूल क्या होगा?

Concept

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Exam Tip

यदि \(x^2-23x+q=0\) का एक मूल (9) है, तो दूसरा मूल क्या होगा?

Concept

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Exam Tip

यदि \(x^2-21x+q=0\) का एक मूल (8) है, तो दूसरा मूल क्या होगा?

Concept

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यदि \(x^2-15x+q=0\) का एक मूल (6) है, तो दूसरा मूल क्या होगा?

Concept

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Exam Tip

यदि \(x^2-9x+q=0\) का एक मूल (4) है, तो दूसरा मूल क्या होगा?

Concept

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Exam Tip

यदि \(x^2-5x+q=0\) का एक मूल (2) है, तो दूसरा मूल क्या होगा?

Concept

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यदि (4x-2-(4h+1)x+h=0) की एक जड़ \(\frac{1}{4}\) है, तो दूसरी जड़ क्या है?

Concept

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Exam Tip

यदि (x-2-(m+9)x+9m=0) की एक जड़ (9) है, तो दूसरी जड़ क्या है?

Concept

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यदि (2x-2-(3p+2)x+p(p+2)=0) की एक जड़ (p) है, तो दूसरी जड़ क्या होगी?

Concept

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यदि (3x-2-(3h+1)x+h=0) की एक जड़ \(\frac{1}{3}\) है, तो दूसरी जड़ क्या है?

Concept

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Exam Tip

यदि (2x-2-(h+1)x+h=0) की जड़ों में से एक हमेशा \(\frac{1}{2}\) है, तो दूसरी जड़ क्या होगी?

Concept

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Exam Tip

यदि (x-2-(m+2)x+3m=0) की एक जड़ (3) है, तो दूसरी जड़ क्या है?

Concept

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यदि (x-2-(m-2)x+m-6=0) की एक जड़ (3) है, तो दूसरी जड़ क्या होगी?

Concept

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यदि \(x^2+ax+12=0\) की एक जड़ दूसरी जड़ से (3) अधिक है, तो (a) के संभव मान क्या हैं?

Concept

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यदि (x-2+(k-3)x+k=0) की एक जड़ दूसरी जड़ की दुगुनी है, तो (k) का मान क्या होगा?

Concept

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यदि \(x^2+ax+a=0\) का एक मूल (2) है तो दूसरा मूल क्या होगा?

Concept

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Exam Tip

यदि \(x^2+ax+a=0\) का एक मूल (1) है तो दूसरा मूल क्या होगा?

Concept

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समीकरण \(x^2-17x+70=0\) का एक मूल (7) है तो दूसरा मूल क्या है?

Concept

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समीकरण \(x^2-15x+54=0\) का एक मूल (6) है तो दूसरा मूल क्या है?

Concept

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समीकरण \(x^2-13x+40=0\) का एक मूल (5) है तो दूसरा मूल क्या है?

Concept

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यदि (4x^-2-(4h+1)x+h=0) की एक जड़ \(\frac{1}{4}\) है, तो दूसरी जड़ क्या है?

यदि (x^-2-(m+9)x+9m=0) की एक जड़ (9) है, तो दूसरी जड़ क्या है?

यदि (2x^-2-(3p+2)x+p(p+2)=0) की एक जड़ (p) है, तो दूसरी जड़ क्या होगी?

यदि (3x^-2-(3h+1)x+h=0) की एक जड़ \(\frac{1}{3}\) है, तो दूसरी जड़ क्या है?

यदि (2x^-2-(h+1)x+h=0) की जड़ों में से एक हमेशा \(\frac{1}{2}\) है, तो दूसरी जड़ क्या होगी?

यदि (x^-2-(m+2)x+3m=0) की एक जड़ (3) है, तो दूसरी जड़ क्या है?

यदि (x^-2-(m^-2)x+m^-6=0) की एक जड़ (3) है, तो दूसरी जड़ क्या होगी?

यदि (x^-2+(k-3)x+k=0) की एक जड़ दूसरी जड़ की दुगुनी है, तो (k) का मान क्या होगा?

यदि (x^-2-(m+7)x+7m=0) का एक मूल (7) है, तो दूसरा मूल क्या है?

यदि (x^-2-(m+6)x+6m=0) का एक मूल (6) है, तो दूसरा मूल क्या है?

यदि (x^-2-(m+5)x+5m=0) का एक मूल (5) है, तो दूसरा मूल क्या है?

यदि (x^-2-(m+4)x+4m=0) का एक मूल (4) है, तो दूसरा मूल क्या है?