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Question

If 12 and 0 are the zeroes of the polynomial f(x)=2x3+ax2+bx+c, and b + c = 2, then the value of b(c – a) is

A
5
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B
2
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C
0
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D
10
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Solution

The correct option is D 10
Given polynomial is f(x)=2x3+ax2+bx+c ...(i)

Also, b + c = 2 ...(ii)

Here, 12 and 0 are zeroes of polynomial f(x).

Putting 0 in (i), we get

f(0)=2(0)3+a(0)2+b(0)+c=0

⇒ c = 0 …..(iii)

From (ii), we have

b + c = 2

⇒ b + 0 = 2

⇒ b = 2 ….. (iv)

Again, 12 is a zero of polynomial f(x), we get

f(12)=2×(12)3+a×(12)2+2×(12)+0=0 (b=2, c=0)

2×18+a×14+1=0

a4+54=0

a=5 ...(v)

b(ca)=2(0(5)) [From (iii), (iv) and (v)]

= 10

Hence, the correct answer is option (d).

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