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).
Related Questions
Assertion (A): Every quadratic equation ax2 + bx + c = 0, a ≠ 0, a, b and c are all real numbers has two real roots.
Reason (R): Every quadratic equation ax2 + bx + c = 0, a ≠ 0, a, b and c are all real numbers has two real roots if 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).
Assertion (A): The quadratic equation 4x2 + 12x + 15 = 0, has no real roots.
Reason (R): The quadratic equation ax2 + bx + c = 0, has real roots iff its '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).
Consider the polynomial 2x2 - 3x + 5
Assertion (A): Factorisation of the above polynomial is not possible.
Reason (R): Discriminant 'b2 - 4ac' is negative.
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).
Consider the following equation k2x2 - 2kx + 1 = 0
Assertion (A): This equation has real roots for all non-zero values of k.
Reason (R): The discriminant of this equation is zero.
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).