Question

If y= 2 and y= 0 are the zeros of the polynomial f(y)= 2y3-5y2+ay+b, find the value of a and b.

Answer 1

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Answer 2

Given : y = 2 and y = 0 are the zeroes of the polynomial f(y) = 2y³ - 5y² + ay + b

To find :  value of a and b.

Solution:

f(y) = 2y³ - 5y² + ay + b

y = 2 and y = 0 are the zeroes of the polynomial

=> f(2) = f(0) = 0

f(0) = 0 - 0 + 0 + b   = 0

=> b = 0

f(y) = 2y³ - 5y² + ay + 0

=>  f(y) = 2y³ - 5y² + ay

f(2) =  = 0

=> 2(2)³  - 5(2)² + a(2)  = 0

=> 16 - 20 + 2a = 0

=> 2a = 4

=> a = 2

a= 2

b = 0

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