Question

Assertion: If a and B are the roots of the equation 13x² − 7x + 1 = 0 then `alpha + beta = 7/13`

Reason: Every quadratic equation has two real roots.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true but Reason (R) is false.

• Assertion (A) is false but Reason (R) is true.

Answer 1

Assertion (A) is true but Reason (R) is false.

Explanation:

Assertion (A):

13x² − 7x + 1 = 0

For a quadratic ax² + bx + c = 0,

`alpha + beta = -b/a`

a = 13, b = −7

`alpha + beta = - (-7)/13 = 7/13`

Assertion (A) is true.

Reason (R):

Every quadratic equation has two real roots.

This is not always true.
A quadratic equation may have:

• two real and distinct roots,

• two equal real roots, or

• no real roots (when discriminant < 0).

Reason (R) is false.