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Question (11)

QN0036631

Find the roots of x²−7x+12=0.

(A) 2, 6
(B) 3, 4
(C) 1, 12
(D) 4, 5

Correct Answer: B

Explanation:

x²−7x+12=(x−3)(x−4). Hence x=3,4.

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Question (12)

QN0036632

The roots of 2x²−7x+3=0 are:

(A) 1, 3/2
(B) 3, 1/2
(C) 2, 3/2
(D) 3, 2

Correct Answer: B

Explanation:

2x²−7x+3=(2x−1)(x−3). Hence x=1/2,3.

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Question (13)

QN0036633

If one root of x²−9x+20=0 is 4, the other root is:

(A) 3
(B) 5
(C) 6
(D) 7

Correct Answer: B

Explanation:

x²−9x+20=(x−4)(x−5). Therefore, the other root is 5.

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Question (14)

QN0036634

For 3x²−10x+3=0, the product of the roots is:

(A) 10/3
(B) 1
(C) 10
(D) 1/3

Correct Answer: B

Explanation:

Product of roots = c/a = 3/3 = 1.

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Question (15)

QN0036635

The equation x²−6x+9=0 has:

(A) Two distinct roots
(B) Two equal roots
(C) No real roots
(D) Three roots

Correct Answer: B

Explanation:

x²−6x+9=(x−3)², so the root 3 is repeated.

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Question (16)

QN0036636

If 2x²+kx+8=0 has equal roots, then k can be:

(A) 4
(B) 8
(C) ±8
(D) ±4

Correct Answer: C

Explanation:

For equal roots, k²−4(2)(8)=0. Thus k²=64 and k=±8.

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Question (17)

QN0036637

For what value of k does x²+kx+16=0 have equal roots?

(A) 4
(B) 8
(C) ±8
(D) ±4

Correct Answer: C

Explanation:

k²−4(1)(16)=0 gives k²=64, so k=±8.

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Question (18)

QN0036638

The equation 2x²−3x+5=0 has:

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

Correct Answer: C

Explanation:

D=(−3)²−4(2)(5)=9−40=−31<0. Hence there are no real roots.

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Question (19)

QN0036639

For 3x²−5x+2=0, the discriminant is:

(A) 1
(B) 5
(C) 7
(D) 9

Correct Answer: A

Explanation:

D=(−5)²−4(3)(2)=25−24=1.

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Question (20)

QN0036640

If D>0 for a quadratic equation, then its roots are:

(A) Equal and real
(B) Distinct and real
(C) Non-real
(D) Always integers

Correct Answer: B

Explanation:

A positive discriminant gives two distinct real roots.

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Question (11)

Find the roots of x²−7x+12=0.

Explanation:

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Question (12)

The roots of 2x²−7x+3=0 are:

Explanation:

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Question (13)

If one root of x²−9x+20=0 is 4, the other root is:

Explanation:

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Question (14)

For 3x²−10x+3=0, the product of the roots is:

Explanation:

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Question (15)

The equation x²−6x+9=0 has:

Explanation:

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Question (16)

If 2x²+kx+8=0 has equal roots, then k can be:

Explanation:

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Question (17)

For what value of k does x²+kx+16=0 have equal roots?

Explanation:

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Question (18)

The equation 2x²−3x+5=0 has:

Explanation:

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Question (19)

For 3x²−5x+2=0, the discriminant is:

Explanation:

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Question (20)

If D>0 for a quadratic equation, then its roots are:

Explanation:

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