Question

find the value of p for which 4x+px+3=0 has equal roots

Answer 1

For the equation to have equal roots it should be in form x² ± 2ax + a² = 0

So,

$= > 4 {x}^{2} + px +3 = 0 \\ \\ = > {x}^{2} + x. \frac{p}{4} + \frac{3}{4} = 0 \\ \\ = > {x}^{2} + 2.x. \frac{p}{8} + {( \frac{ \sqrt{3} }{2} )}^{2} = 0$

Thus comparing we get,

$= > \bf \frac{p}{8} = \frac{ \sqrt{3} }{2} \\ \\ = > \bf p = 8 \times \frac{ \sqrt{3} }{2} = \underline{4 \sqrt{3} }$
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