Question

If x = 0 and x = - 1 are the roots of the polynomial f(x) = $2x^3-3x^2$ + ax + b, find the value of a and b.

Answer 1

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

$\because$ x = 0 and x = - 1 are its zeros

$\therefore$ f (0) = 0 and f(-1) = 0

Now, f(0) = 0

$\Rightarrow 2(0{)}^3-3(0{)}^2+a\times$ 0 + b = 0

$\Rightarrow$ 0 - 0 + 0 + b = 0

$\therefore$ b = 0

and f(-1) = 0

$\Rightarrow 2(-2{)}^3-3(-1{)}^2$ + a (-1) + b = 0

$\Rightarrow 2\times (-1)-3\times 1+a\times$ (-1) + b = 0

$\Rightarrow$ -2 - 3 - a + b =0

$\Rightarrow -2-3-a=0\Rightarrow$ a = - 5

$\Rightarrow -5-a=0\Rightarrow$ a = - 5

Hence a = - 5, b = 0