Mathematics
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).
Answer
The quadratic equation: ax2 + bx + c = 0.
The expression b2 - 4ac is called the discriminant (D).
When,
D > 0; two distinct real roots
D = 0; real and equal roots
D < 0; then roots are imaginary
thus, assertion (A) is false but reason(R) is true.
Hence, option 2 is the correct option.
Related Questions
If x2 + kx + 6 = (x - 2)(x - 3) for all values of x, then the value of k is :
-5
-3
-2
5
The roots of quadratic equation x2 - 1 = 0 are :
0
1
-1
±1
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).
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).