# Q1.    Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:                (i)    $2x^2 - 3x +5 = 0$

D Divya Prakash Singh

For a quadratic equation,  $ax^2+bx+c = 0$ the value of discriminant determines the nature of roots and is equal to:

$D = b^2-4ac$

If D>0 then roots are distinct and real.

If D<0 then no real roots.

If D= 0 then there exists two equal real roots.

Given the quadratic equation,  $2x^2 - 3x +5 = 0$.

Comparing with general to get the values of a,b,c.

$a = 2, b =-3,\ c= 5$

Finding the discriminant:

$D= (-3)^2 - 4(2)(5) = 9-40 = -31$

$\because D<0$

Here D is negative hence there are no real roots possible for the given equation.

Exams
Articles
Questions