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Mathematics

Assertion (A): For the trinomial 2x2 + 8x - 9 cannot be factorised.

Reason (R): For trinomial ax2 + bx + c to be factorised, b2 - 4ac must be a perfect square.

  1. Assertion (A) is true, Reason (R) is false.

  2. Assertion (A) is false, Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

Factorisation

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Answer

For trinomial ax2 + bx + c to be factorised, the roots are given by the quadratic equation: x = −b±b2−4ac2a\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

For the trinomial ax2 + bx + c to be factorizable into linear factors with rational coefficients, its roots must be rational numbers. This occurs if and only if the expression the discriminant b2 - 4ac, is a perfect square.

∴ Reason (R) is true.

For the trinomial 2x2 + 8x - 9, a = 2, b = 8 and c = -9.

D = b2 - 4ac

= 82 - 4 × 2 × -9

= 64 + 72

= 136.

Since, 136 is not a perfect square. So, 2x2 + 8x - 9 cannot be factorised.

∴ Assertion (A) is true.

∴ Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

Hence, option 3 is the correct option.

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