Question

Assertion: The roots of the equation x² − 4x + 3 = 0 are 1 and 3.

Reason: If ax² + bx + c = 0, a ≠ 0 then roots are given by `x =(-b+-sqrt(b^2-4ac))/(2a)`.

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

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

Explanation:

Assertion (A):

x² − 4x + 3 = 0

(x − 1) (x − 3) = 0

So, the roots are 1 and 3.

Assertion (A) is true.

Reason (R):

The quadratic formula for ax² + bx + c = 0 is:

`x = (-b +- sqrt(b^2 - 4ac))/(2a)`

Reason (R) is also true.

This formula is the general method used to find the roots of any quadratic equation, including the given one, hence it explains the assertion.