Question

if 4x^2 - 12x + k is a perfect square , find the value of k

Answer 1

Step-by-step explanation:

4x^2 - 12x + k

=> b^2 - 4ac

=> (-12)^2 - 4(4)(k)

=> 144 - 16k

=> 144 = 16k

=> 144/16 = k

=> k = 9 ( k is a perfect square )

Hope it helps you

Answer 2

The value of k for the quadratic equation to be perfect square is 9

Step-by-step explanation:

Given as :

The quadratic equation is

4 x² - 12 x + k  = 0

According to question

The equation is a perfect square

For quadratic equation to be perfect square the discriminant of the equation should be zero

i.e Discriminant = D = 0

∵   D = b² - 4 a c   satisfy for the quadratic equation a x² + b x + c  = 0

So, By compare the equation we ,get

   D = ( - 12 ) ² - 4 × 4 × k

And ∵  D = 0

So,      ( - 12 ) ² - 4 × 4 × k = 0

or,      144 - 16 k = 0

Or,      - 16 k = - 144

Or,            k = $\dfrac{144}{16}$

∴               k = 9

So, The value of k = 9

Hence, The value of k for the quadratic equation to be perfect square is 9 Answer