Question

The roots of the quadratic equation $2x^2+5x-3=0$ are -3 and .

• A. $\frac{1}{2}$
• B. 3
• C. 6

Answer 1

The correct option is A $\frac{1}{2}$

Consider the quadratic equation $2x^2+5x-3=0.$
We first reduce this equation to a form wherein the coefficient of $x^2$ equals 1.
$⟹x^2+\frac{5}{2}x-\frac{3}{2}=0$
$⟹x^2+\frac{5}{2}x+(\frac{5}{4}{)}^2-(\frac{5}{4}{)}^2-\frac{3}{2}=0$
$⟹x^2+2\left(x\right)\left(\frac{5}{4}\right)+(\frac{5}{4}{)}^2-(\frac{5}{4}{)}^2-\frac{3}{2}=0$
$⟹(x+\frac{5}{4}{)}^2-\frac{49}{16}=0$
$⟹(x+\frac{5}{4}{)}^2=\frac{49}{16}$
$⟹x+\frac{5}{4}=\pm \frac{7}{4}$
$\therefore x=\frac{1}{2},-3$