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[[1]] is the value of p for which the quadratic equation 4x2+px+3=0 has equal roots.

Subtopics: Finding square root by division method

see full answer

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Detailed Solution

Given, the equation as 4x2+px+3=0
If ax2+bx+c=0 is a quadratic equation, then roots of the equation is given by

x = \frac{- b \pm \sqrt{b^{2} - 4 ac}}{2 a}

………. (i)
Comparing the general equation with the given equation we get
a=4
b=p
c=3
Now putting these values in equation (i), we get the roots of the equations as,

x = \frac{- p \pm \sqrt{p^{2} - 4 * 4 * 3}}{2 * 4}

⇒

x = \frac{- p \pm \sqrt{p^{2} - 48}}{8}

We get two roots,
x1 =

\frac{- p + \sqrt{p^{2} - 48}}{8}

and x2 =

\frac{- p - \sqrt{p^{2} - 48}}{8}

For the two roots to be equal, we observe that the term

\sqrt{p^{2} - 48}

of both the roots should be zero which would give us

x 1 = x 2

.
Equating

\sqrt{p^{2} - 48}

to zero, we get

\sqrt{p^{2} - 48}

= 0
⇒p2−48=0
⇒p2=48

\Rightarrow p = \pm \sqrt{48}

\Rightarrow p = \pm 4 \sqrt{3}

Therefore, the value of p for which the roots are equal is

\pm 4 \sqrt{3}

So, the correct answer is “

\pm 4 \sqrt{3}

”.

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