Question

A quadratic equation 2x² + 5x − 3 = 0. 

Assertion (A): The roots of the equation 2x² + 5x − 3 = 0 are real and unequal.

Reason (R): For the equation ax² + bx +c = 0, the roots are real and unequal if b² − 4ac > 0.

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Given, 2x² + 5x − 3 = 0

As we know that the roots of equation ax² + bx + c = 0 are real and unequal if b² − 4ac > 0.

⇒ b² − 4ac = 5² − 4 × 2 ×x (−3)

= 25 + 24

= 49 > 0

So, Assertion (A) is true.

And Reason (R) is also true and correctly explains the assertion, as (b² − 4ac > 0) means that the roots are real and different.