Question

If the quadratic equation px^2 - 2√5px + 15 = 0 has two equal real roots, then find the value of p

Answer 1

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We know that, General form of quadratic equations is $\bf{ax^2+bx+c=0}$

So, on comparing the given equation that is px² -2√5 px + 15 = 0  we get

a = p , b = -2√5 , c = 15

Now, If the roots of a quadratic equation are equal then its discriminant ( D )= 0

On solving ,

D = 0

b² - 4ac = 0

So, ( -2√5 p )² - 4×p ×15 = 0

=> 20p² - 60p = 0

=> 20p( p - 3) = 0

20p = 0 and ( p - 3 ) = 0

Therefore, p = 0 or p = 3

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Answer 2

Answer: p=0 or p=3

here, a=p, b=-2root5 p, c=15

if equation has 2 real roots then, Discriminant is greater than or equal to zero.

Discriminant (D)=  b² - 4ac = 0

   =>   ( -2√5 p )² - 4×p ×15 = 0

                  => 20p² - 60p = 0

                   => 20p( p - 3) = 0

         20p = 0 and ( p - 3 ) = 0

Therefore, p = 0 or p = 3

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