Find the values of k for which the quadratic equation 3`x^2` + `kx` + 3 = 0 has real and equal roots.
Given,
3`x^2` + `kx` + 3 = 0
Comparing with `ax^2` - `bx` + `c` = 0
So, a = 3, b = k and c = 3
We Know that, when the equation has 2 equal roots,
D = 0
⇒ `"b"^2`- 4ac = 0
⇒ `"k"^2`- 4 `\times`3 `\times`3 = 0
⇒ `"k"^2`- 36
⇒ k = ` \pm\sqrt{36}`
⇒ k = ` \pm 6`
Hence, the values of k for which the quadratic equation 3`x^2` + `kx` + 3 = 0 has real and equal roots are 6 or -6.