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RD Chapter 2 Polynomials Ex MCQS Solutions

Question - 11 : -

If the product of zeros of the polynomial f(x) = ax3 – 6x2 + 11x – 6 is 4, then a =

Answer - 11 : - (a)

f(x) = ax3 – 6x2 + 11x – 6


Question - 12 : -

If zeros of the polynomial f(x) = x3 – 3px2 + qx – r are in AP, then
(a) 2p3 = pq – r
(b) 2p3 = pq + r
(c) p3 = pq – r
(d) None of these

Answer - 12 : - (a)

 f(x) = x3 – 3px2 + qx – r
Here a = 1, b = -3p, c = q, d= -r
Zeros are in AP
Let the zeros be α – d, α, α + d


Question - 13 : -

If the product of two zeros of the polynomial f(x) = 2x3 + 6x2 – 4x + 9 is 3, then its third zero is

Answer - 13 : - (b)


Question - 14 : - If the polynomial f(x) = ax2 + bx – c is divisible by the polynomialg(x) = ax2 + bx + c, then ab =

Answer - 14 : - (a)



Question - 15 : -
In Q. No. 14, ac =
(a) b
(b) 2b
(c) 2b2
(d) -2b

Answer - 15 : -

(b) In the previous questions
Remainder = 0
(b – ac + ab2) = 0
b + ab2 = ac
=> ac = b (1 + ab) = b (1 + 1) = 2b

Question - 16 : -

If one root of the polynomial f(x) = 5x2 + 13x + k is reciprocal of the other, then the value of k is
(a) 0
(b) 5
(c) 1/6

(d) 6

Answer - 16 : - (b)


Question - 17 : - If α, β, γ are the zeros of the polynomial f(x)= ax3 + bx2 + cx + d, then 

Answer - 17 : - (c)


Question - 18 : -

If α, β, γ are the zeros of the polynomial f(x) = ax3 + bx2 + cx + d, then α2 + β2 + γ2 =

Answer - 18 : - (d)



Question - 19 : - If α, β, γ are the zeros of the polynomial f(x)= x3 – px2 + qx – r, then 

Answer - 19 : - (b)


Question - 20 : - If α, β are the zeros of the polynomial f(x) = ax2 + bx + c, then 

Answer - 20 : - (b)


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