Question

Check whether the equation $6x^2-7x+2=0$ has real roots. If it has, find them by method of completing square.

Answer 1

$6x^2-7x+2$

Condition for real roots

$b^2>4ac(-7{)}^2>4(6\left)\right(2)49>48$

$6x^2-7x+2=0x^2-\frac{7}{6}x+\frac{1}{3}=0x^2-\frac{7}{6}x=-\frac{1}{3}{x}^2-2\left(1\right)\frac{7}{12}x+{\left(\frac{7}{12}\right)}^2=\frac{-1}{3}+{\left(\frac{7}{12}\right)}^2{(x-\frac{7}{12})}^2=\frac{1}{144}x-\frac{7}{12}=\pm \frac{1}{12}x=\frac{2}{3},\frac{1}{2}$