Q1 of 46 Page 1

If the quadric equation px2 – 2√5px + 15 = 0 has two equal roots, then find the value of p.

We know that for a quadratic equation in the form


ax2 + bx + c = 0 has equal roots if


D = 0


where D = discriminant


and


D = b2 - 4ac


Given equation is px2 - 2√5px + c = 0


a = p


b = - 2√5p


c = 15


D = ( - 2√5p)2 - 4(p)(15)


D = 20p2 - 60p


As equation has real roots


If D = 0


20p2 - 60p = 0


20p(p - 3) = 0


p = 0 or p = 3


But p = 0 is not possible otherwise given equation will not be quadratic.


 

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