Question

if -1 and 1 are the zeros of the polynomial f(x) =3x^3 -2x^2+ax-b . find the values of a and b

Answer 1

Answer:

$f(x) =3x^3 -2x^2+ax-b$

-1,1 are zeroes of f(x)

-1,1 are zeros of polynomial f(x)

so

$f(-1)=3( { - 1)}^{3} - 2 {(1)}^{2} + a( - 1) - b$

$0 = - 3 - 2 - a - b$

$- a - b = 5.......eq1$

$f(1) = 3 {(1)}^{3} - 2{(1)}^{2} + a - b$

$0 = 3 - 2 + a - b$

$a - b = - 1........eq2$

$eq1 + 2$

$- 2b = 4$

$b = - 2$

$a = </strong><strong>-3</strong><strong>$