Question

Determine the value of 'p' for which the equation
2x square + 4 root3x + p = 0 has equal roots.​

Answer 1

➺Given :

•The Quadratic equation =$\bf{2x^{2}+4\sqrt{3}x+p=0 }$

➺To find :

•The value of 'p'=?

➺Solution :

⇒Given Quadratic equation $\bf{2x^{2}+4\sqrt{3}x+p=0}$

⇒The nature of the equation are equal .

Hence, the determinant $\red{\bf{D=0}}$

$\\ \\ \implies\green{\bf{D=b^{2}-4ac}}$

$\\ \\ \implies\sf{D=(4\sqrt{3})^{2}-4(2)(p) =0}$

$\\ \\ \implies\sf{D=48-8p=0}$

$\\ \\ \implies\sf{8p=48}$

$\\ \\ \implies\boxed{\sf{p=6}}$

Nature of the Roots:

$\\ \\ \bf{\blue{(1) b^{2}-4ac=0 }\quad ......The \: roots \: real \: and \: equal }$

$\\ \\ \bf{\blue{(2) b^{2}-4ac>0 } \quad ......The \: roots \: real \: and \: distinct }$

$\\ \\ \bf{\blue{(2) b^{2}-4ac<0} \: \quad ......The \: roots \: are \: imaginary }$