Question

Find the value of k, if the roots of the quadratic equation 3x 2 - k x + 48 = 0 Are real and equal​

Answer 1

Answer:

k=24

Step-by-step explanation:

3x²-kx+48=0

a=3, b=(-k), c=48

The roots are real and equal

b²-4ac=0

(-k)²-4(3)(48)=0

k²-576=0

k²=576

k=√576

k=24

Therefore, the value of k is 24.

Answer 2

Given:

3x 2 - k x + 48 = 0

To find:

The value of k

Solution:

The required value of k is ±24.

We know that the given equation can have roots that are real and equal when its discriminant equals 0.

Here, the given equation is-

$3x^{2}$-kx+48=0

So, the discriminant's value=$b^{2}$-4ac

From the equation, a= 3, b= -k, and c=48.

Using the values, we get

Discriminant's value=, D$(-k)^{2}$-4×3×48

=$k^{2}$ -576

Since D=0, we will equate them.

$k^{2}$ -576=0

$k^{2}$ =576

k=±24

Therefore, the required value is ±24.