Question

for what values of a quadratic equation 9 x square - 3 ax + 1 equal to zero has equal roots ​please answer very fast

Answer 1

Answer:

The values of a are 2, -2

Step-by-step explanation:

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:

a = ± 2

Step-by-step explanation:

let the zeros be p and q

equating p(X) with ax² + bx + c = 0

we get a = 9, b = -3a, c = 1

p= q ---------------(1)

p + q = - b / a ----(2)

therefore from 1 and 2

p+p = -(-3a)/ 9

2p = 3a/9

2p = a/3 ----------------(3)

p*q = c/a

p*p = 1/9

p² = ±1/9

p = + 1/3 & p = -1/3

put this in 3

when p = +1/3

2p = a/3

2*1/3 = a/3

2/3 = a/3

a = 2

when p= -1/3

2p = a/3

2 *(-1/3) = a/3

-2/3= a/3

a = -2