Question

Assertion: Equation 3x³ + x² − 1 = (x + 1)³ is quadratic.

Reason: The equation ax² + bx + c = 0, a ≠ 0 is quadratic.

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 false but Reason (R) is true.

Explanation:

Assertion (A):

3x³ + x² − 1 = (x + 1)³

Expand the RHS:

(x + 1)³ = x³ + 3x² + 3x + 1

3x³ + x² − 1 − (x³ + 3x² + 3x + 1) = 0

2x³ − 2x² − 3x − 2 = 0

The highest power of x is 3, so the equation is cubic, not quadratic.

Assertion (A) is false.

Reason (R):

The equation ax² + bx + c = 0, a ≠ 0 is quadratic.

This is the correct definition of a quadratic equation.

Reason (R) is true.