Question

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them.

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

Answer 1

Evaluate the discriminant to identify if the equation has real roots:

We know that discriminant $D=b^2-4ac$

The condition to have real roots in a quadratic equation is $D\ge 0$.

Given equation, $2x^2-3x+5=0$, where $a=2,b=-3,c=5$

So, the discriminant will be,

$$\begin{gathered} \Rightarrow D={(-3)}^2-(4\times 2\times 5) \\ \Rightarrow D=9-40 \\ \Rightarrow D=-31 \end{gathered}$$

As $D<0$, so the given equation doesn't satisfy the required condition to have real roots.

Hence, $2x^2-3x+5=0$ doesn't have real roots.