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 $b$.



Given :

The given polynomial is $f(x) = 2x^3 - 3x^2 + ax + b$.

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

To find :

We have to find the values of $a$ and $b$.

Solution :

The zero of the polynomial is defined as any real value of $x$, for which the value of the polynomial becomes zero.

Therefore,

Zero of the polynomial $f(0)= 2(0)^3-3(0)^2+a(0)+b=0$

$0-0+0+b=0$

$b=0$

$f(-1)= 2(-1)^3-3(-1)^2+a(-1)+b=0$

$2(-1)-3-a+0=0$

$a=-2-3$

$a=-5$

The values of $a$ and $b$ are $-5$ and $0$ respectively.  

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