Q9 of 50 Page 1

Find the values of p for which the quadratic equation 4x2 + px + 3 = 0 has equal roots.

Given quadratic equation 4x2 + px + 3 = 0


Also given the equation has equal roots.


We know that a quadratic equation ax2 + bx + c = 0 has two equal roots, if b2 – 4ac = 0.


Comparing the given equation, we get


a = 4; b = p and c = 3


⇒ p2 – 4(4)(3) = 0


⇒ p2 – 48 = 0


⇒ p2 = 48


⇒ p = ± 4√3


∴ The values of p are 4√3 and -4√3.


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