Question

find the values of k such that the roots of equation kx^2-4x+2=0 real and equal.​

Answer 1

Solution:

Given Equation:

→ kx² - 4x + 2 = 0

Comparing with ax² + bx + c = 0, we get:

→ a = k

→ b = -4

→ c = 2

Therefore, the discriminant of the equation will be:

→ D = b² - 4ac

→‎ D = 16 - 8k

Since, the roots are real and equal, discriminant must be equal to zero.

→ 16 - 8k = 0

→ 8k = 16

→ k = 2

★ So, the value of k for which the roots are real and equal is 2.

Answer:

• The value of k is 2.

To Know More:

Standard form of a quadratic equation is:

$\rm \longrightarrow a {x}^{2} + bx + c = 0$

Roots of the equation is given as:

$\rm \longrightarrow x_{1,2} = \dfrac{ - b \pm \sqrt{D} }{2a}$

Where:

$\rm \longrightarrow D = {b}^{2} - 4ac$

And is commonly known as the discriminant.

1) When D > 0, roots are real and distinct.

2) When D = 0, roots are real and equal.

3) When D < 0, roots are imaginary.

The roots of the quadratic equation have sum equal to the expression -b/a and product equal to c/a.