A quadratic equation ax² + bx + c = 0 ; where a, b and c are real numbers and a ≠ 0.

Assertion (A): The roots of 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.

1. A is true, R is false.

2. A is false, R is true.

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

4. Both A and R are true and R is incorrect reason for A.

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

Reason

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 x 2 x (-3)

= 25 + 24 = 49 > 0

So, Assertion (A) is true.

And, Reason (R) is also true and it clearly explain assertion as a positive discriminant (b² - 4ac > 0) guarantees that the roots are real and unequal

Hence, option 3 is correct.