Question

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them;
(i) $2x^2-3x+5=0$

Answer 1

(i) Consider the equation
$2x^2-3x+5=0$
Comparing it with (ax^2 + bx + c = 0\), we get
a = 2, b = -3 and c = 5
$Discriminant\left(D\right)=b^2-4ac$
$=(-3{)}^2-4(2\left)\right(5)=9-40$
$=-31$
$Since,D<0$,
Therefore, no real root is possible for the given equation.