Q. 14.6( 15 Votes )

# 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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