Question:
If polynomial 6x^4+ 8x^3-5x^2 +ax+ b is exactly divisible by polynomial 2x^2-5 then find a and b
Answer:
Given, the polynomial 6x4 + 8x3 - 5x2 + ax + b is exactly divisible by polynomial 2x2 - 5
So, the remainder should be zero.
Now,
Since the remainder should be zero
=> (20 + a)x + 25 + b = 0
Now, the coefficient of x and constant term both should be equal to zero
=> 20 + a = 0
=> a = -20
and 25 + b = 0
=> b = -25
So, the value of and b are -20 and -25 respectively.
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