Question

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

find them: 2x

2 + x + 4​

Answer 1

Question :-

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

2x² + x + 4

Answer :-

To determine the nature of roots, we have to find the value of discriminant :-

→ D = b² - 4ac

For the given equation :-

• a = 2
• b = 1
• c = 4

→ D = 1² - 4 × 2 × 4

→ D = 1 - 32

→ D = -31

Here, the value of discriminant is negative. So, the roots are imaginary.

Additional information :-

Nature of the roots of the quadratic expression.

1. If D > 0 then roots are real and different.

2. If D is a perfect square, then roots are rational and different.

3. If D = 0, then roots are real and equal.

4. If D < 0 then, roots are imaginary and unequal or complex conjugate.