Maths Class 10th
Chapter 2
Polynomials
Q.1 The graphs of y = P(x) are given in the figure given below, for some polynomials P(x) find the number of the zeros of P(x) in each case,
Sol. The number of zeros is 3 as graph intersects or cuts the x-axis at three points only.
Q. 2 Find the quadratic polynomial each with the given number as the sum and product of its zeros respectively.
(i) x² –2x –8
Sol.
Q. 3 Find the quadratic polynomial each with the given number as its zeros respectively.
(i) 1/4, –1
Sol.
Q. 4 Find the quadratic polynomial each with the given number as the sum and the product of its zeros respectively.
(i) ✓2, 1/3
Sol.
Sum of zero = ✓2
Product of zero = 1/3
Equation
x² –(Sum of zero)x + (Product of zero)
= x² – (✓2)x + (1/3)
=3/3[ x² – (✓2)x + (1/3)]
=1/3[ 3 × x² – 3 × (✓2)x + 3 × (1/3)]
=1/3[ 3x² – 3 ✓2 x + 1]
equation
= 3x² – 3 ✓2 x + 1
where 1/3 is a real constant.
Q.5 Divide 2x⁴ – 3x³–3x² + 6x – 2 by 2x² – 3x +1
Sol.
Q. 6 Find all the zeros of 2x⁴ – 3 x³–x² + 6x – 2, if you know that two of its zeros are √2 and – √2.
Sol.
Q.7 Find all the zeros of 3x⁴ + 6x³ – 2x² –10x – 5, if you know that two of its zeros are √(5/3) and – √(5/3).
Sol.
Q. 8 On dividing x³ – 3x² + x + 2, by polynomial g(x) the quotient and reminder were (x – 2) and (– 2x + 4) respectively. Find g(x).
Sol.
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