Sum

If the quadratic equation px^{2} − 2√5px + 15 = 0 has two equal roots then find the value of p.

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#### Solution

Given quadratic equation is, px² -2√5 px + 15 = 0

Compare px² -2√5 px + 15 = 0 with ax² + bx + c = 0

a = p , b = -2√5p , c = 15

We know that , If the roots of the quadratic equation are equal , then it's discriminant (D) equals to zero.

discriminant = 0

b² - 4ac = 0

( -2√5 p )² - 4× p × 15 = 0

20p² - 60p = 0

20p ( p - 3 ) = 0

p - 3 = 0

p = 3

Concept: Nature of Roots

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