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Q.

The polynomial P(x) = x3 + ax2 + bx + c has the property that the mean of its roots, the product of its roots, and the sum of its coefficients are all equal. If the y-intercept of the group of y = P(x) is 2 then

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a

b=-11

b

c=2

c

P(1)=-2

d

a=6

answer is A, B, C, D.

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Detailed Solution

p(x)=x3+ax2+bx+c
α,β,γ are the roots
α+β+γ3=αβγ=1+a+b+c………(1)
y-Intercept of p(x) =2 ⇒ c=2
α+β+γ=−6
a=6
from (1) 1 + a + b + c = –2
1 + 6 + b + 2 = –2
b = –11

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