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Andreyy89
2 years ago
14

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

Mathematics
1 answer:
klasskru [66]2 years ago
7 0
<h3><u>Correct Questions :- </u></h3>

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

<h3><u>Solution</u>:- </h3>

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 \times 4 \times 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=±\sqrt{48}\end{gathered}

\begin{gathered}\implies\quad \sf  p=±\sqrt{2 \times 2 \times 2 \times 2 \times 3} \end{gathered}

\begin{gathered}\implies\quad \sf  p=± 2\times 2\sqrt{ 3 }\end{gathered}

\begin{gathered}\implies\quad \boxed{\sf{p=±4\sqrt{ 3 }}}\end{gathered}

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

4√3 and -4√3.

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