Mathematics
Assertion (A): The roots of the quadratic equation 3x2 + 7x + 8 = 0 are imaginary.
Reason (R): The discriminant of a quadratic equation is always positive.
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
Answer
Given,
⇒ 3x2 + 7x + 8 = 0
Comparing 3x2 + 7x + 8 = 0 with ax2 + bx + c = 0 we get,
a = 3, b = 7 and c = 8.
We know that,
Discriminant (D) = b2 - 4ac
= (7)2 - 4 × (3) × (8)
= 49 - 96 = -47; which is negative.
Therefore, the equation has imaginary and unequal roots.
So, Assertion (A) is true.
The Discriminant of quadratic equation can be positive, negative or equal to zero.
So, Reason (R) is false.
A is true, R is false.
Hence, option 3 is the correct option.
Related Questions
Assertion (A): The quadratic equation 3kx2 - 4kx + 4 = 0 has equal roots, if k = 3.
Reason (R): For equal roots of a quadratic equation, we must have D = 0.
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.