Question

For what values of 'a' the quadratic equation 9x² - 3ax + 1 = 0 has equal
roots ?​

Answer 1

Answer:

The values of a are 2, -2

Step-by-step explanation:

Concept used:

If $b^2-4ac=0$ then roots of the quadraatic equation $ax^2+bx+c=0$ are equal

Given:

$9x^2-3ax+1=0$ has equal roots

since the roots are equal, $b^2-4ac=0$

$\implies\:(-3a)^2-4*9*1=0$

$\implies\:9a^2-36=0$

$\implies\:9a^2=36$

$\implies\:a^2=4$

$\implies\:a=2,-2$

Answer 2

Answer:

Step-by-step explanation:

Concept used:

If b^2-4ac=0b

2

−4ac=0 then roots of the quadraatic equation ax^2+bx+c=0ax

2

+bx+c=0 are equal

Given:

9x^2-3ax+1=09x

2

−3ax+1=0 has equal roots

since the roots are equal, b^2-4ac=0b

2

−4ac=0

\implies\:(-3a)^2-4*9*1=0⟹(−3a)

2

−4∗9∗1=0

\implies\:9a^2-36=0⟹9a

2

−36=0

\implies\:9a^2=36⟹9a

2

=36

\implies\:a^2=4⟹a

2

=4

\implies\:a=2,-2⟹a=2,−2