Question

Find zero's and verify relation between ,
(a)$6x^2+5x-1=0$
(b)$11x^2-8x-3=0$

Answer 1

(a)$6x^2+5x-1=0$
$6x^2+6x-x-1=0$
$6x(x+1)-1(x+1)=0$
$(6x-1)(x+1)=0$
$x=\frac{1}{6},-1$
$\frac{1}{6}+(-1)=\frac{-b}{a}=\frac{-5}{6}$
$\frac{-5}{6}=\frac{-5}{6}$
$\frac{1}{6}\times (-1)=\frac{c}{a}=\frac{-1}{6}$
$\frac{-1}{6}=\frac{-1}{6}$
hence verified.
(b)$11x^2-8x-3=0$
$11x^2-11x+3x-3=0$
$11x(x-1)+3(x-1)=0$
$(11x+3)(x-1)=0$
$x=\frac{-3}{11},1$
$\frac{-3}{11}+1=\frac{-b}{a}=\frac{8}{11}\frac{8}{11}=\frac{8}{11}\frac{-3}{11}\times 1=\frac{c}{a}=\frac{-3}{11}\frac{-3}{11}=\frac{-3}{11}$
hence verified.