Finding coefficients of polynomials with given zeros?

Question

Find the values of a and b such that 1 and 4 are zeros of f(x) = 2x^4 - 5x^3 - 14x^2 + ax +b. 

Thank you!

 

 

Answer 1

Step 1 :

The polynomial equation is .

The zeros of the polynomial are and

If is a solution of the equation then .

Consider a zero .

Substiute the value in the equation .

Consider a zero .

Substiute the value in the equation .

Step 2 :

Sove the equations and to find the values of  and .

Substiute the value  in equation :

Solution :

The values of and  are and .