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Question (31)

QN0036551

For p(x) = x³ - 4x, the number of distinct zeroes is:

(A) 1
(B) 2
(C) 3
(D) 4

Correct Answer: C

Explanation:

x³ - 4x = x(x - 2)(x + 2). Therefore, the zeroes are 0, 2 and -2.

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Question (32)

QN0036552

If p(x) = x³ - x², its zeroes are:

(A) 0 and 1
(B) 1 and -1
(C) 0 and -1
(D) 1 only

Correct Answer: A

Explanation:

x³ - x² = x²(x - 1), so the zeroes are 0 and 1.

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Question (33)

QN0036553

The maximum possible number of zeroes of a cubic polynomial is:

(A) 1
(B) 2
(C) 3
(D) 4

Correct Answer: C

Explanation:

A polynomial of degree 3 can have at most 3 zeroes.

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Question (34)

QN0036554

If the graph of a cubic polynomial crosses the x-axis at x = -2, 0 and 3, then its zeroes are:

(A) -2 and 3 only
(B) 0 and 3 only
(C) -2, 0 and 3
(D) -2, 3 and 6

Correct Answer: C

Explanation:

The x-coordinates of the points where the graph intersects the x-axis are the zeroes.

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Question (35)

QN0036555

For 2x³ - 5x² - 14x + 8, the sum of the zeroes is:

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

Correct Answer: B

Explanation:

Sum of zeroes = -b/a = -(-5)/2 = 5/2.

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Question (36)

QN0036556

For 2x³ - 5x² - 14x + 8, the product of the zeroes is:

(A) 4
(B) -4
(C) 8
(D) -8

Correct Answer: B

Explanation:

Product of zeroes = -d/a = -8/2 = -4.

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Question (37)

QN0036557

If α, β and γ are zeroes of 3x³ + 7x² - 2x + 5, then α + β + γ is:

(A) 7/3
(B) -7/3
(C) 2/3
(D) -2/3

Correct Answer: B

Explanation:

α + β + γ = -b/a = -7/3.

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Question (38)

QN0036558

If α, β and γ are zeroes of 4x³ - 9x² + 6x - 8, then αβ + βγ + γα is:

(A) -9/4
(B) 9/4
(C) 3/2
(D) -3/2

Correct Answer: C

Explanation:

αβ + βγ + γα = c/a = 6/4 = 3/2.

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Question (39)

QN0036559

If the zeroes of x³ - 6x² + 11x - 6 are α, β and γ, then αβγ equals:

(A) 6
(B) -6
(C) 11
(D) -11

Correct Answer: A

Explanation:

αβγ = -d/a = -(-6)/1 = 6.

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Question (40)

QN0036560

If the zeroes of a cubic polynomial are 1, 2 and 4, then the coefficient of x² in a monic polynomial having these zeroes is:

(A) 7
(B) -7
(C) 8
(D) -8

Correct Answer: B

Explanation:

Sum of zeroes = 1 + 2 + 4 = 7. Hence the coefficient of x² is -7.

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Question (31)

For p(x) = x³ - 4x, the number of distinct zeroes is:

Explanation:

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Question (32)

If p(x) = x³ - x², its zeroes are:

Explanation:

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Question (33)

The maximum possible number of zeroes of a cubic polynomial is:

Explanation:

Link:

Question (34)

If the graph of a cubic polynomial crosses the x-axis at x = -2, 0 and 3, then its zeroes are:

Explanation:

Link:

Question (35)

For 2x³ - 5x² - 14x + 8, the sum of the zeroes is:

Explanation:

Link:

Question (36)

For 2x³ - 5x² - 14x + 8, the product of the zeroes is:

Explanation:

Link:

Question (37)

If α, β and γ are zeroes of 3x³ + 7x² - 2x + 5, then α + β + γ is:

Explanation:

Link:

Question (38)

If α, β and γ are zeroes of 4x³ - 9x² + 6x - 8, then αβ + βγ + γα is:

Explanation:

Link:

Question (39)

If the zeroes of x³ - 6x² + 11x - 6 are α, β and γ, then αβγ equals:

Explanation:

Link:

Question (40)

If the zeroes of a cubic polynomial are 1, 2 and 4, then the coefficient of x² in a monic polynomial having these zeroes is:

Explanation:

Link:

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