Question

for what values of "a "does the equation 9 x ^2 - 2 X + a = 6-ax possess equal roots.

Answer 1

heya man !! how's going on !!!!

9x² -2x + a = 6 - ax have equal roots

now,
9x² - 2x + a -( 6 - ax) = 0

9x² -(2 -a)x +( a - 6) = 0
you can see this , this is in the form of quadratic equation .
we know ,
roots are equal in quadratic equation when , D = b² - 4ac = 0
where ,
b is coefficient of x
a is coefficient of x²
c is constant .

(2 - a)² - 4(a - 6)9 = 0
4 + a² -4a -36a +216 = 0
a² -40a + 220 = 0
a = { 40 ±√(1600-880)}/2
= (20 ± √180)

hope that helps !!!!

@ himanshu Jha ✌