Question

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

Answer 1

px^2-3px+9=0
condition for equal roots are b^2-4ac
here,a=p
b=3p
c=9
(3p)^2-4*p*9
= 9p^2-36p
=9p(p-4)
= p=0 or p= 4

Answer 2

px ( x - 3 ) + 9 = 0

px² - 3px + 9 = 0


• When roots are equal then the discriminant is equal to Zero.

D = 0

D = b² - 4ac

0 = ( - 3p )² - 4 × p × 9


0 = 9p² - 36p

0 = 9p ( p - 4 )

• 9p = 0

p = 0


• ( p - 4 ) = 0

p = 4


So, for both the value of p the equation have equal roots.