Polynomials
Previous Year Solved Questions 2020
1. The degree of polynomial having zeroes -3 and 4 only is: [CBSE 2020]
(a) 2 (b) 1 (c) more than 3 (d) 3
(a) 2 (b) 1 (c) more than 3 (d) 3
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Ans: (a) 2
Two distinct zeroes → minimum degree 2
Simplest polynomial: (x+3)(x-4) = x² – x – 12 (degree 2)
Two distinct zeroes → minimum degree 2
Simplest polynomial: (x+3)(x-4) = x² – x – 12 (degree 2)
2. If one of the zeroes of the quadratic polynomial x² + 3x + k is 2, then the value of k is: [CBSE 2020]
(a) 10 (b) -10 (c) -7 (d) -2
(a) 10 (b) -10 (c) -7 (d) -2
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Ans: (b) -10
Since 2 is a zero:
f(2) = 2² + 3×2 + k = 0
4 + 6 + k = 0
10 + k = 0
k = -10
Since 2 is a zero:
f(2) = 2² + 3×2 + k = 0
4 + 6 + k = 0
10 + k = 0
k = -10
Q3: The quadratic polynomial, the sum of whose zeroes is -5 and their product is 6 is: [CBSE 2020]
(a) x² + 5x + 6 (b) x² – 5x + 6 (c) x² – 5x – 6 (d) -x² + 5x + 6
(a) x² + 5x + 6 (b) x² – 5x + 6 (c) x² – 5x – 6 (d) -x² + 5x + 6
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Ans: (a) x² + 5x + 6
Sum = -5, Product = 6
Polynomial: x² – (sum)x + (product)
= x² – (-5)x + 6
= x² + 5x + 6
Sum = -5, Product = 6
Polynomial: x² – (sum)x + (product)
= x² – (-5)x + 6
= x² + 5x + 6
Q4: Form a quadratic polynomial, the sum and product of whose zeroes are (-3) and 2 respectively. [CBSE 2020]
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Ans: x² + 3x + 2
Sum = -3, Product = 2
Polynomial: x² – (sum)x + (product)
= x² – (-3)x + 2
= x² + 3x + 2
Sum = -3, Product = 2
Polynomial: x² – (sum)x + (product)
= x² – (-3)x + 2
= x² + 3x + 2
Q5: The zeroes of the polynomial x² – 3x – m(m+3) are: [CBSE 2020]
(a) m, m+3 (b) -m, m+3 (c) m, -(m+3) (d) -m, -(m+3)
(a) m, m+3 (b) -m, m+3 (c) m, -(m+3) (d) -m, -(m+3)
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Ans: (b) -m, m+3
Solve x² – 3x – m(m+3) = 0
Discriminant = 9 + 4m(m+3) = (2m+3)²
Roots = [3 ± (2m+3)]/2
= (3+2m+3)/2 = m+3
and (3-2m-3)/2 = -m
Solve x² – 3x – m(m+3) = 0
Discriminant = 9 + 4m(m+3) = (2m+3)²
Roots = [3 ± (2m+3)]/2
= (3+2m+3)/2 = m+3
and (3-2m-3)/2 = -m