Mathematics
Assertion (A): 3x2 - 8x - 15 is not factorisable.
Reason (R): The trinomial ax2 + bx + c is factorisable, if the value of b2 - 4ac, where a = coefficient of x2, b = coefficient of x, c = constant, is perfect square, otherwise not.
- A is true, R is false.
- A is false, R is true.
- Both A and R are true.
- Both A and R are false.
Factorisation
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Answer
Both A and R are true.
Explanation
Comparing 3x2 - 8x - 15 with ax2 + bx + c, we get:
a = 3, b = -8 and c = -15
⇒ b2 - 4ac
⇒ (-8)2 - 4 x 3 x (-15)
⇒ 64 + 180
⇒ 244
Since 244 is not a perfect square, the equation 3x2 - 8x - 15 is not factorisable.
∴ Assertion (A) is true.
ax2 + bx + c, where a, b and c are real numbers, is known as a trinomial or a quadratic expression in which a = coefficient of x2, b = coefficient of x and c = constant.
If we find the value of b2 - 4ac and this value is a perfect square, the trinomial ax2 + bx + c is factorisable, otherwise, not.
∴ Reason(R) is true.
Hence, both Assertion (A) and Reason (R) are true.
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