Question

For what value of p the equation
9x^2–3 (p-1)x+(p-1)=o has real and equal roots.​

Answer 1

Step-by-step explanation:

equation has equal root means

D = b^2 - 4ac = 0

comparing equation by

ax^2+ bx +c = 0

a = 9 , b = 3 (p-1 ) , c = ( p-1 )

[3 (p-1)]^2 - 4× 9 × (p-1) = 0

[ 3p-1] ^2 - 36 ( p- 1)= 0

9p ^2 +1 - 2× 3p ×1 =0

9p^2 - 6p + 1 = 0

9p^2 - 3p - 3p + 1 = 0

3p ( 3p- 1) -1 (3p - 1) =0

( 3p -1 ) (3p - 1) =0

3p - 1 =0

3p = 1

p= 1/3