Find the value of (K² − 5), if the quadratic equation 2x² − 8x + K = 0 has real and equal roots.

Correct option is B

Given:

The quadratic equation 2x² − 8x + K = 0 has real and equal roots.

Concept Used:

Condition for Real and Equal Roots
For a quadratic equation ax² + bx + c = 0, the condition for real and equal roots is given by the discriminant (Δ):
Δ = b² - 4ac 
For real and equal roots, Δ must be equal to 0:
Δ = 0 

Solution:
Apply the Condition to the Given Equation
In the equation 2x² - 8x + K = 0, we have:
a = 2, b = -8, c = K
Substitute these values into the discriminant formula:
Δ = (-8)² - 4 × 2 × K
Δ = 64 - 8K
For real and equal roots, Δ = 0, so:
64 - 8K = 0
8K = 64
K = 64 / 8 = 8
Then the value of  (K² - 5)
Now, calculate (K² - 5):
K² - 5 = 8² - 5 = 64 - 5 = 59
The value of (K² - 5) is 59.