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Class 10 Maths Chapter 2: Polynomials MCQs with answers

10 multiple-choice questions on Polynomials, each with its answer and the reason, written from the NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
The degree of the polynomial 3 − 5y + 2y4 − y2 is
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Answer: (b) 4

The highest power of y that appears is y4, so the degree is 4. The terms need not be in order.

Question 2
Which of the following is not a polynomial?
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Answer: (d) 2x + 3x

3x = 3x−1 puts the variable in a denominator, so 2x + 3x is not a polynomial. Irrational or fractional coefficients (√7, 12, 15) are allowed.

Question 3
ax3 + bx2 + cx + d, with a, b, c, d real, is a cubic polynomial provided
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Answer: (a) a ≠ 0

Only the coefficient of the highest power must be non-zero; if a = 0 the degree drops below 3. The other coefficients may be zero (x3 − 8 is a cubic).

Question 4
If p(x) = 2x2 − 5x + 3, then p(−2) equals
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Answer: (c) 21

p(−2) = 2(−2)2 − 5(−2) + 3 = 8 + 10 + 3 = 21. Taking (−2)2 as −4 or −5(−2) as −10 gives the distractors.

Question 5
Which of the following is a zero of x2 + 2x − 15?
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Answer: (a) 3

p(3) = 9 + 6 − 15 = 0, so 3 is a zero. p(5) = 20, p(−3) = −12, p(15) = 240. (x2 + 2x − 15 = (x + 5)(x − 3).)

Question 6
The zero of the linear polynomial 5x + 4 is
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Answer: (a) −45

The zero of ax + b is −ba = −45. Check: 5(−45) + 4 = 0.

Question 7
The graph of y = p(x) for a quadratic polynomial p(x) is shown. The zeroes of p(x) are
xyO−4−3−2−1123−6−4−2246
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Answer: (a) −3 and 2

The zeroes are the x-coordinates of the points where the graph meets the x-axis: −3 and 2. The y-intercept −6 is p(0), not a zero, and a zero is a number, not a point.

Question 8
The graph of y = −3x2 + x + 5 is a parabola that
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Answer: (b) opens downwards

For y = ax2 + bx + c the parabola opens downwards when a < 0. Here a = −3.

Question 9
The graph of y = p(x) for a quadratic polynomial p(x) is shown. The number of zeroes of p(x) is
xyO−1123452468
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Answer: (b) 0

The parabola lies entirely above the x-axis and never meets it, so p(x) has no zero. The lowest point (2, 2) is a turning point, not a zero.

Question 10
A polynomial p(x) has degree 5. The greatest number of points at which the graph of y = p(x) can meet the x-axis is
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Answer: (d) 5

A polynomial of degree n has at most n zeroes, so its graph meets the x-axis at most n times: here at most 5.

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