Question

Find a polynominal $f\left(x\right)$ of degree $2$ where $f\left(0\right)=8,f\left(1\right)=12,f\left(2\right)=18$.

• A. $x^2+3x-8$
• B. $x^2-3x+8$
• C. $2x^2-x+3$
• D. $x^2+3x+8$

Answer 1

The correct option is D $x^2+3x+8$

Let the polynomial is $a{x}^2+bx+c$.
Now, $f\left(0\right)=8$
$\Rightarrow c=8$
$\therefore$ Equation is $a{x}^2+bx+8$.
Again, $f\left(1\right)=12\Rightarrow a+b+8=12$
$\Rightarrow a+b=4$ $.....\left(i\right)$
and $f\left(2\right)=18$
$\Rightarrow 4a+2b+8=18$
$\Rightarrow 2a+b=5$ ......$\left(ii\right)$
On solving Eqs. $\left(i\right)$ and $\left(ii\right)$, we get
$a=1,b=3$
$\therefore$ Required equation is $x^2+3x+8$.