Question

Find the value of k, if the quadratic equation
$3x {}^{2} - k \sqrt{3} x + 4 = 0$
Has equal roots ​

Answer 1

Finding value of k , in

given Quadratic equation:

Compare $3x {}^{2} - k \sqrt{3} x + 4 = 0$

with ax²+bx+c = 0 ,we get

a=3, b =k√3 , c = 4,

Discriminant (D)=0

[ Since , given roots are equal]

b² - 4ac = 0

=> (k√3)² - 4×3×4 = 0

=> 3k² - 48 = 0

=> 3[ k² - 16 ] = 0

=> k² - 16 = 0

=> k² = 16

=> k = ± √16

=> k = ± 4

Therefore ,

k = -4 or k = 4

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