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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 10Given 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(c−a)=2(0−(−5)) [From (iii), (iv) and (v)] = 10 Hence, the correct answer is option (d).

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