Question

if the polynomial p(x)=6x4+8x3+-5x2+ax+b is exactly divisible by 2x2-5 then find the values of a and b

Answer 1

Hey Mate Here Is Your Answer,

When we divide 6x4 + 8x3 – 5x2 + ax + b by the polynomial 2x2 – 5, we get

Quetient = 3x2 + 4x + 5

and Remainder = (20 + a)x + (25 + b)

Given, the polynomial 6x4 + 8x3 – 5x2 + ax + b is exactly divisible by the polynomial 2x2 – 5

So, the remainder should be zero

Hence, (20 + a)x + (25 + b) = 0

=> 20 + a = 0

=> a = -20

and 25 + b = 0

=> b = -25

So, the value of a is -20 and b is -25

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