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RD Chapter 2 Polynomials Ex MCQS Solutions

Question - 1 : -

If α, β are the zeros of the polynomial f(x) = x2 + x + 1, then 

 (a) 1
(b) -1
(c) 0
(d) None of these

Answer - 1 : -



Question - 2 : -

If α, β are the zeros of the polynomial p(x) = 4x2 + 3x + 7, then  isequal to

Answer - 2 : -

(d)

Question - 3 : -

If one zero of the polynomial f(x) = (k2 + 4) x2 + 13x + 4k is reciprocal of the other, thenk =
(a) 2
(b) -2
(c) 1
(d) -1

Answer - 3 : - (a)

f (x) = (k2 + 4) x2 + 13x + 4k
Here a = k2 + 4, b = 13, c = 4k
One zero is reciprocal of the other
Let first zero = α

RD Sharma Class 10 Solutions Chapter 2 Polynomials MCQS 3
K = 2

Question - 4 : -

If the sum of the zeros of the polynomial f(x) = 2x3 – 3kx2 + 4x – 5 is 6, then value of k is
(a) 2
(b) 4
(c) -2
(d) -4

Answer - 4 : - (b) 


Question - 5 : -

If α and β are the zeros of the polynomial f(x) = x2 + px + q, then a polynomial having α and β is its zerosis
(a) x2 + qx + p
(b) x2 – px + q
(c) qx2 + px + 1
(d) px2 + qx + 1

Answer - 5 : - (c)


Question - 6 : -

If α, β are the zeros of polynomial f(x) = x2 – p (x + 1) – c, then (α + 1) (β + 1) =
(a) c – 1
(b) 1 – c
(c) c
(d) 1 + c

Answer - 6 : - (b)


Question - 7 : -

If α, β are the zeros of the polynomial f(x) = x2 – p(x + 1) – c such that (α + 1) (β + 1) = 0, then c =
(a) 1
(b) 0
(c) -1
(d) 2

Answer - 7 : - (a)



Question - 8 : -

If f(x) = ax2 + bx + c has no real zeros and a + b + c< 0, then
(a) c = 0
(b) c > 0
(c) c < 0
(d) None of these

Answer - 8 : - (d)

 f(x) = ax2 + bx + c
Zeros are not real
b2 – 4ac < 0 ….(i)
but a + b + c < 0
b < – (a + c)
Squaring both sides b2 < (a + c)2
=> (a + c)2 – 4ac < 0 {From (i)}
=> (a – c)2 < 0
=> a – c < 0
=> a < c

Question - 9 : -

If the diagram in figure shows the graph of the polynomialf(x) = ax2 + bx + c, then
(a) a > 0, b < 0 and c > 0
(b) a < 0, b < 0 and c < 0
(c) a < 0, b > 0 and c > 0
(d) a < 0, b > 0 and c < 0

Answer - 9 : - (a)

Curve ax2 + bx + c intersects x-axis at two points andcurve is upward.
a > 0, b < 0 and c> 0

Question - 10 : -

Figure shows the graph of the polynomial f(x) = ax2 + bx + c for which
(a) a < 0, b > 0 and c > 0
(b) a < 0, b < 0 and c > 0
(c) a < 0, b < 0 and c < 0
(d) a > 0, b > 0 and c < 0

Answer - 10 : - (b)

Curve ax2 + bx + c intersects x-axis at two points andcurve is downward.
a < 0, b < 0 and c > 0

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