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Question
For what values of k are the roots of the quadratic equation `3x^2+2kx+27` real and equal ?
Solution
Given:
`3x^2+2kx+27=0`
Here,
`a =3,b=2k and c=27`
It is given that the roots of the equation are real and equal; therefore, we have:
`D=0`
⇒`(2k)^2-4xx3xx27=0`
⇒`4k^2-324=0`
⇒`4k^2=324`
⇒`k^2=81`
⇒ `k=+-9`
∴ `k=9 or k=-9`
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