Q14 of 50 Page 1

Find the value of p so that the quadratic equation px (x – 3) + 9 = 0 has equal roots.

Given quadratic equation px (x – 3) + 9 = 0


⇒ px2 – 3px + 9 = 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 = p; b = -3p and c = 9


⇒ (-3p)2 – 4(p)(9) = 0


⇒ 9p2 – 36p = 0


⇒ 9p (p – 4) = 0


⇒ p = 0 and 4


∴ The values of p are 0 and 4.


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