Question

If the polynomial 6x4 + 8x3- 5x2 + ax + +b is exactly divisible by the polynomial 2x2 - 5 , then find the value of a and b



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Answer 1

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

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