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Question (31)

QN0036651

The roots of x²−11x+30=0 are:

(A) 4 and 7
(B) 5 and 6
(C) 3 and 10
(D) 2 and 15

Correct Answer: B

Explanation:

x²−11x+30=(x−5)(x−6). Hence the roots are 5 and 6.

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Question (32)

QN0036652

If one root of 2x²−9x+10=0 is 2, the other root is:

(A) 2
(B) 5/2
(C) 3
(D) 4

Correct Answer: B

Explanation:

2x²−9x+10=(2x−5)(x−2). Hence the other root is 5/2.

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Question (33)

QN0036653

The roots of 6x²−x−2=0 are:

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

Correct Answer: A

Explanation:

6x²−x−2=(3x−2)(2x+1). Hence x=2/3 and −1/2.

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Question (34)

QN0036654

The equation x²−10x+25=0 can be written as:

(A) (x+5)²=0
(B) (x−5)²=0
(C) (x−25)(x−1)=0
(D) (x−10)(x+25)=0

Correct Answer: B

Explanation:

x²−10x+25=(x−5)².

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Question (35)

QN0036655

For which value of k will x²−2(k+1)x+k²=0 have equal roots?

(A) 1/2
(B) 1
(C) −1/2
(D) 2

Correct Answer: C

Explanation:

Equal roots require 4(k+1)²−4k²=0. Thus 2k+1=0, so k=−1/2.

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Question (36)

QN0036656

If x=3 is a root of 2x²+kx−15=0, then k equals:

(A) −1
(B) 1
(C) 3
(D) 5

Correct Answer: A

Explanation:

2(3)²+3k−15=0 gives 18+3k−15=0, so k=−1.

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Question (37)

QN0036657

For what value of k does x²+4x+k=0 have no real roots?

(A) k<4
(B) k=4
(C) k>4
(D) k=0

Correct Answer: C

Explanation:

D=16−4k. For no real roots, 16−4k<0, so k>4.

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Question (38)

QN0036658

If x²−6x+k=0 has two distinct real roots, then:

(A) k>9
(B) k=9
(C) k<9
(D) k=0 only

Correct Answer: C

Explanation:

D=36−4k>0, hence k<9.

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Question (39)

QN0036659

If x²+px+9=0 has equal roots, then p can be:

(A) 3 only
(B) −3 only
(C) ±6
(D) ±3

Correct Answer: C

Explanation:

For equal roots, p²−36=0. Therefore p=±6.

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Question (40)

QN0036660

The equation 4x²+4x+1=0 has roots:

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

Correct Answer: D

Explanation:

4x²+4x+1=(2x+1)². Hence x=−1/2 is the repeated root.

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Question (31)

The roots of x²−11x+30=0 are:

Explanation:

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Question (32)

If one root of 2x²−9x+10=0 is 2, the other root is:

Explanation:

Link:

Question (33)

The roots of 6x²−x−2=0 are:

Explanation:

Link:

Question (34)

The equation x²−10x+25=0 can be written as:

Explanation:

Link:

Question (35)

For which value of k will x²−2(k+1)x+k²=0 have equal roots?

Explanation:

Link:

Question (36)

If x=3 is a root of 2x²+kx−15=0, then k equals:

Explanation:

Link:

Question (37)

For what value of k does x²+4x+k=0 have no real roots?

Explanation:

Link:

Question (38)

If x²−6x+k=0 has two distinct real roots, then:

Explanation:

Link:

Question (39)

If x²+px+9=0 has equal roots, then p can be:

Explanation:

Link:

Question (40)

The equation 4x²+4x+1=0 has roots:

Explanation:

Link:

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