Mathematics
Assertion (A): The equation 9x2 + 6x - k = 0 has real roots if k ≥ -1.
Reason (R): The quadratic equation ax2 + bx + c = 0 has real roots if 'discriminant' = b2 - 4ac > 0.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Quadratic Equations
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Answer
We know that,
The quadratic equation ax2 + bx + c = 0 has real roots if 'discriminant' = b2 - 4ac ≥ 0.
So, reason (R) is false.
Given, 9x2 + 6x - k = 0
Comparing above equation with ax2 + bx + c = 0, we get :
a = 9, b = 6 and c = -k
If the equation has real roots, then D ≥ 0
⇒ b2 - 4ac ≥ 0
⇒ 62 - 4 x 9 x (-k) ≥ 0
⇒ 36 + 36k ≥ 0
⇒ 36k ≥ -36
⇒ k ≥ -
⇒ k ≥ -1
So, assertion (A) is true.
Thus, Assertion (A) is true, but Reason (R) is false.
Hence, option 1 is the correct option.
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