Question

The equation formed by decreasing each root of ax${}^2$ + bx + c= $0$ by $1$ is $2$x${}^2$ + $8$x + $2$ =$0$. then find the values of a,b and c.

Answer 1

$2x^2+8x+2=0$

$\Rightarrow x^2+4x+1=0$

$\therefore x=\frac{-4\pm \sqrt{16-4}}{2}=\frac{-4\pm \sqrt{12}}{2}=\frac{-4\pm 2\sqrt{3}}{2}$

$=-2\pm \sqrt{3}$

$\therefore$Roots of $a{x}^2+bx+c=0$ are $-3+\sqrt{3}$ &

$-3-\sqrt{3}$

$\therefore a{x}^2+b{x}^2+c=0=(x+(3+\sqrt{3}))(x+(3+\sqrt{3}))$

$=x^2+3x-\sqrt{3}x+3x+\sqrt{3}x+9-3\sqrt{3}+3\sqrt{3}-3$

$=+6x+6$

$\therefore a=1;b=6;c=6$