For what values of k will the quadratic 9x^2 +12x +k^2 = 0 have 2 real solutions?

Braeden Valenzuela

Braeden Valenzuela

Answered question

2022-09-04

For what values of k will the quadratic 9 x 2 + 12 x + k 2 = 0 have 2 real solutions?

Answer & Explanation

Adrienne Sherman

Adrienne Sherman

Beginner2022-09-05Added 9 answers

For any quadratic equation
a x 2 + b x + c = 0 ,   a 0
If b 2 4 a c is positive i.e, b 2 4 a c > 0 we get two real solution
Given, 9 x 2 + 12 x + k 2 = 0
here, a = 9 ,   b = 12 ,   c = k 2
For two real solution
b 2 4 a c > 0 ( 12 ) 2 4 × 9 × k 2 > 0 144 36 k 2 > 0 144 > 36 k 2 36 k 2 < 144 k 2 < 144 36 k 2 < 4 2 < k < 2 k ( 2 , 2 )

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