Question

In a polynomial P(x)=2x³+ax²-7x+b and P (1)= 3, P (2)= 19 .
Then find value of a and b​.​

Answer 1

Answer:

Let P(x) = 2x^3 + ax^2 + bx - 6

If x-1 is a factor of P(x) then the sum of the coefficients of P(x) = 0

So 2 + a + b - 6 = 0 => a+b = 4 ……..(1)

When P(x) is divided by x-2 then the remainder is 2.

Then by remainder theorem P(2) = 2

2×2^3 + a×2^2+2b-6 = 2

=> 4a + 2b = -8 => 2a + b = -4 ……(2)

(2) - (1) gives a = -8 and using this in (1) we get b = 12

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