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Question
For what values of p are the roots of the equation `4x^2+px+3=0` real and equal?
Solution
The given equation is `4x^2+px+3=0`
This is of the form `ax^+bx+c=0` where `a=4, b=p and c=3`
∴` D=b^2-4ac=p^2-4xx4xx3=p^2-48`
The given equation will have real and equal roots if D = 0.
∴ `p^2-48=0`
⇒`p^2=48`
⇒`p=+-sqrt48=+-4sqrt3`
Hence, `4sqrt3` and `-4sqrt3` are the required values of p.
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