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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