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Question (41)

QN0036661

The discriminant of 5x²+2x−3=0 is:

(A) 16
(B) 64
(C) 4
(D) 36

Correct Answer: B

Explanation:

D=2²−4(5)(−3)=4+60=64.

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Question (42)

QN0036662

For 4x²+4x+3=0, the nature of roots is:

(A) Two distinct real roots
(B) Two equal real roots
(C) No real roots
(D) One root is zero

Correct Answer: C

Explanation:

D=4²−4(4)(3)=16−48=−32<0. Hence there are no real roots.

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Question (43)

QN0036663

A pole is placed on the boundary of a circular park whose diameter is 13 m. Its distances from two diametrically opposite gates differ by 7 m. If its distance from one gate is x, which quadratic equation results?

(A) x²+7x−60=0
(B) x²−7x−60=0
(C) x²+14x−169=0
(D) 2x²+7x−60=0

Correct Answer: A

Explanation:

If the distances are x and x+7, Pythagoras gives x²+(x+7)²=13², which simplifies to x²+7x−60=0.

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Question (44)

QN0036664

For the equation x²+7x−60=0, the positive root is:

(A) 4
(B) 5
(C) 10
(D) 12

Correct Answer: B

Explanation:

x²+7x−60=(x+12)(x−5). The roots are −12 and 5. Since distance is positive, x=5.

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Question (45)

QN0036665

If x²+7x−60=0 represents the distances of a pole from two gates, the two distances are:

(A) 5 m and 7 m
(B) 5 m and 12 m
(C) 7 m and 12 m
(D) 12 m and 17 m

Correct Answer: B

Explanation:

The positive root is x=5. The other distance is x+7=12 m.

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Question (46)

QN0036666

The quadratic formula can be applied to ax²+bx+c=0 to obtain real roots when:

(A) b²−4ac<0
(B) b²−4ac≥0
(C) a=0
(D) c=0 only

Correct Answer: B

Explanation:

For real roots, the discriminant b²−4ac must be non-negative.

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Question (47)

QN0036667

If x²−8x+k=0 has equal roots, the value of k is:

(A) 8
(B) 12
(C) 16
(D) 32

Correct Answer: C

Explanation:

Equal roots require 64−4k=0, so k=16.

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Question (48)

QN0036668

A quadratic equation has roots 3 and 7. Which equation could represent it?

(A) x²−10x+21=0
(B) x²+10x+21=0
(C) x²−4x+21=0
(D) x²+4x−21=0

Correct Answer: A

Explanation:

Sum of roots=10 and product=21. Therefore the equation is x²−10x+21=0.

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Question (49)

QN0036669

A quadratic equation has one root 4 and the product of its roots is 12. The other root is:

(A) 2
(B) 3
(C) 4
(D) 6

Correct Answer: B

Explanation:

Product of roots=12. If one root is 4, the other root=12/4=3.

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Question (50)

QN0036670

A rectangular mango grove has length twice its breadth and area 800 m². Which pair gives its dimensions?

(A) 10 m, 80 m
(B) 15 m, 30 m
(C) 20 m, 40 m
(D) 25 m, 50 m

Correct Answer: C

Explanation:

Let breadth=x and length=2x. Then 2x²=800, giving x=20 m and length=40 m.

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Question (41)

The discriminant of 5x²+2x−3=0 is:

Explanation:

Link:

Question (42)

For 4x²+4x+3=0, the nature of roots is:

Explanation:

Link:

Question (43)

A pole is placed on the boundary of a circular park whose diameter is 13 m. Its distances from two diametrically opposite gates differ by 7 m. If its distance from one gate is x, which quadratic equation results?

Explanation:

Link:

Question (44)

For the equation x²+7x−60=0, the positive root is:

Explanation:

Link:

Question (45)

If x²+7x−60=0 represents the distances of a pole from two gates, the two distances are:

Explanation:

Link:

Question (46)

The quadratic formula can be applied to ax²+bx+c=0 to obtain real roots when:

Explanation:

Link:

Question (47)

If x²−8x+k=0 has equal roots, the value of k is:

Explanation:

Link:

Question (48)

A quadratic equation has roots 3 and 7. Which equation could represent it?

Explanation:

Link:

Question (49)

A quadratic equation has one root 4 and the product of its roots is 12. The other root is:

Explanation:

Link:

Question (50)

A rectangular mango grove has length twice its breadth and area 800 m². Which pair gives its dimensions?

Explanation:

Link:

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