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Question (21)

QN0036541

A quadratic polynomial has zeroes 5 and -2. Which polynomial represents it?

(A) x² - 3x - 10
(B) x² + 3x - 10
(C) x² - 7x + 10
(D) x² + 7x - 10

Correct Answer: A

Explanation:

The polynomial is (x - 5)(x + 2) = x² - 3x - 10.

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Question (22)

QN0036542

A quadratic polynomial has zeroes 1/2 and 3. Taking the coefficient of x² as 2, the polynomial is:

(A) 2x² - 7x + 3
(B) 2x² + 7x + 3
(C) 2x² - 5x + 3
(D) 2x² + 5x - 3

Correct Answer: A

Explanation:

Sum = 7/2 and product = 3/2. Hence polynomial = 2x² - 7x + 3.

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Question (23)

QN0036543

If the sum of zeroes of a quadratic polynomial is 6 and their product is 8, one such polynomial is:

(A) x² + 6x + 8
(B) x² - 6x + 8
(C) x² + 8x + 6
(D) x² - 8x + 6

Correct Answer: B

Explanation:

Polynomial = x² - (sum)x + product = x² - 6x + 8.

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Question (24)

QN0036544

A quadratic polynomial has zeroes -4 and -1. Its constant term, when the coefficient of x² is 3, is:

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

Correct Answer: C

Explanation:

Product of zeroes = (-4)(-1) = 4 = c/3. Therefore, c = 12.

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Question (25)

QN0036545

If the zeroes of 5x² - 13x + 6 are α and β, then 1/α + 1/β is:

(A) 13/6
(B) 5/6
(C) 13/5
(D) 6/13

Correct Answer: A

Explanation:

1/α + 1/β = (α + β)/(αβ) = (13/5)/(6/5) = 13/6.

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Question (26)

QN0036546

If α and β are zeroes of x² - 6x + 5, then α² + β² equals:

(A) 26
(B) 36
(C) 25
(D) 31

Correct Answer: A

Explanation:

α + β = 6 and αβ = 5. Therefore, α² + β² = (α + β)² - 2αβ = 36 - 10 = 26.

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Question (27)

QN0036547

If α and β are zeroes of 2x² - 5x + 2, then α²β + αβ² equals:

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

Correct Answer: A

Explanation:

α²β + αβ² = αβ(α + β) = 1 × 5/2 = 5/2.

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Question (28)

QN0036548

If the zeroes of x² - 8x + k differ by 2, then k is:

(A) 12
(B) 15
(C) 16
(D) 18

Correct Answer: B

Explanation:

(α - β)² = (α + β)² - 4αβ. Thus 4 = 64 - 4k, giving k = 15.

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Question (29)

QN0036549

If one zero of x² - 6x + k is twice the other, then k is:

(A) 4
(B) 6
(C) 8
(D) 9

Correct Answer: A

Explanation:

Let the zeroes be t and 2t. Then 3t = 6, so t = 2. Therefore, k = t(2t) = 4.

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Question (30)

QN0036550

If the zeroes of x² + px + q are equal, then:

(A) p² = 4q
(B) p² = -4q
(C) p = 4q
(D) q = 0

Correct Answer: A

Explanation:

Equal zeroes imply the discriminant condition p² - 4q = 0. Hence p² = 4q.

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Question (21)

A quadratic polynomial has zeroes 5 and -2. Which polynomial represents it?

Explanation:

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Question (22)

A quadratic polynomial has zeroes 1/2 and 3. Taking the coefficient of x² as 2, the polynomial is:

Explanation:

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Question (23)

If the sum of zeroes of a quadratic polynomial is 6 and their product is 8, one such polynomial is:

Explanation:

Link:

Question (24)

A quadratic polynomial has zeroes -4 and -1. Its constant term, when the coefficient of x² is 3, is:

Explanation:

Link:

Question (25)

If the zeroes of 5x² - 13x + 6 are α and β, then 1/α + 1/β is:

Explanation:

Link:

Question (26)

If α and β are zeroes of x² - 6x + 5, then α² + β² equals:

Explanation:

Link:

Question (27)

If α and β are zeroes of 2x² - 5x + 2, then α²β + αβ² equals:

Explanation:

Link:

Question (28)

If the zeroes of x² - 8x + k differ by 2, then k is:

Explanation:

Link:

Question (29)

If one zero of x² - 6x + k is twice the other, then k is:

Explanation:

Link:

Question (30)

If the zeroes of x² + px + q are equal, then:

Explanation:

Link:

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