Question

The given quadratic equations have real roots and the roots are $1$, $\frac{2}{3}$:
$3x^2$ - 5x + 2 = 0

• A. True
• B. False

Answer 1

The correct option is A True

$3x^2-5x+2=0$

$\Rightarrow$ $3x^2-3x-2x+2=0$

$\Rightarrow$ $3x(x-1)-2(x-1)=0$

$\Rightarrow$ $(x-1)(3x-2)=0$

$\Rightarrow$ $x-1=0$ and $3x-2=0$

$\therefore$ $x=1$ and $x=\frac{2}{3}$

$\Rightarrow$ Hence, we can see roots of given quadratic equation are real and roots are $1,\frac{2}{3}$