Question

The equation 12x2 + 4kx + 3 = 0 has real and equal
roots, if
1. k = u00b13
2. k = u00b19
3. k = 4.
4. k = u00b12​

Answer 1

Answer :

k = ± 3

Solution :

Here ,

The given quadratic equation is ;

12x² + 4kx + 3 = 0 .

Now , comparing the given quadratic equation with the general quadratic equation ax² + bx + c = 0 , we have ;

a = 12

b = 4k

c = 3

Now ,

The discriminant of the given quadratic equation will be ;

=> D = b² - 4ac

=> D = (4k)² - 4×12×3

=> D = 16k² - 144

=> D = 16(k² - 9)

Also ,

For the given quadratic equation to have real and equal roots , its discriminant must be zero .

Thus ,

=> D = 0

=> 16(k² - 9) = 0

=> k² - 9 = 0/16

=> k² - 9 = 0

=> k² = 9

=> k = √9

=> k = ± 3

Hence , k = ± 3