Find the values of k for which the quadratic equation 3x2+kx+3=0 has real and equal roots - Bzziii.com

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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.

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