For what positive value of k, does the equation 3x2 + 2kx + 3=0 have real and equal roots?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 3.
Quadratic equation: 3x2 + 2kx + 3 = 0
For a quadratic equation ax2 + bx + c = 0, the discriminant = b2 - 4ac
If the roots are real and equal, the discriminant = 0
Here, a = 3, b = 2k, and c = 3
So, b2 - 4ac = 0
⇒ (2k)2 - 4(3)(3) = 0
⇒ 4k2 - 36 = 0
⇒ 4k2 = 36
⇒ k2 = 36/4 = 9
⇒ k = √9 = 3
The positive value of k for which the equation has real and equal roots is 3.