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  4. If f(x) = 2x2 + bx + c and f(0)=3 and f (2)=1, then f(1) is equal to

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Q. If $f(x) = 2x^{2} + bx + c$ and $f(0)=3$ and $f (2)=1$, then $f(1)$ is equal to

Relations and Functions

Solution:

$f\left(x\right) = 2x^{2} + bx + c$,
$f\left(0\right)=3$
$\Rightarrow 3=c$
and $f\left(2\right) = 1$
$\Rightarrow 1=8+2b+c$
$\Rightarrow 2b+3=-7$
$\Rightarrow b=-5$
$\therefore f\left(1\right)=2\times1^{2}+\left(-5\right)\times1+3=2-5+3$
$=0$.