Mathematics
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).
Quadratic Equations
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Answer
For, the quadratic equation: ax2 + bx + c = 0. The equation has real roots if
b2 - 4ac ≥ 0
So, reason (R) is true.
Comparing equation 4x2 + 12x + 15 = 0, with ax2 + bx + c = 0, we get :
a = 4, b = 12, c = 15
D = b2 - 4ac
= 122 - 4 x 4 x 15
= 144 - 240 = -96.
Since, D < 0, so the equation has no real roots.
So, assertion (A) is true and reason (R) correctly explains assertion (A).
Thus, both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Hence, option 3 is the correct option.
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Related Questions
The roots of quadratic equation x2 - 1 = 0 are :
0
1
-1
±1
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 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).
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).