Question

Find the values of P for which the quadratic equation 4x²+px+3=0?​

Answer 1

Correct Questions :-

Find the values of P for which the quadratic equation 4x²+px+3=0 , provided that roots are equal or discriminant is zero .

Solution:-

Let us Consider a quadratic equation αx² + βx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

For equal roots

• D = 0

`\quad\green{ \underline { \boxed{ \sf{Discriminant, D = β² - 4αc}}}}`

So,

`\sf{ β² - 4αc = 0}`

Here,

• α = 4
• β = p
• c = 3

Now,

`\begin{gathered}\implies\quad \sf p²- 4 * 4 * 3 =0 \end{gathered}`

`\begin{gathered}\implies\quad \sf p²- 48 =0 \end{gathered}`

`\begin{gathered}\implies\quad \sf p²=48\end{gathered}`

`\begin{gathered}\implies\quad \sf p=±√(48)\end{gathered}`

`\begin{gathered}\implies\quad \sf p=±√(2 * 2 * 2 * 2 * 3) \end{gathered}`

`\begin{gathered}\implies\quad \sf p=± 2* 2√( 3 )\end{gathered}`

`\begin{gathered}\implies\quad \boxed{\sf{p=±4√( 3 )}}\end{gathered}`

Thus, the values of P for which the quadratic equation 4x²+px+3=0 are-

4√3 and -4√3.