Question

Find nature of roots of 2x^2+3x+2

Answer 1

$\large\underline{\sf{Solution-}}$

Given quadratic expression is

$\rm :\longmapsto\:f(x) = {2x}^{2} + 3x + 2$

We know

Nature of roots depends upon the Discriminant of quadratic equation.

Let us consider a quadratic polynomial, f(x) = ax² + bx + c, then nature of roots of quadratic polynomial depends upon Discriminant (D).

If Discriminant, D > 0, then roots of the equation are real and distinct.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac

Here,

$\rm :\longmapsto\:a = 2$

$\rm :\longmapsto\:b = 3$

$\rm :\longmapsto\:c = 2$

So,

$\rm :\longmapsto\:Discriminant, D = {b}^{2} - 4ac$

$\rm \:  =  \:  \: {(3)}^{2} - 4 \times 2 \times 2$

$\rm \:  =  \:  \: 9 - 16$

$\rm \:  =  \:  \: - 7$

$\bf\implies \:Discriminant, D = - 7 < 0$

Hence,

Roots are unreal or complex or imaginary.