Question

Values of k for which the quadratic equation 2x^2 – kx + k = 0 has equal roots is
(A) 0 only (B) 4 (C) 8 only (D) 0, 8 7

Answer 1

Equation:

☛ 2x² - kx + k = 0

On comparing with standard from of quadratic equation ( i.e., ax² + bx + c = 0 ) , We get

a = 2 , b = -k , c = k

For equal roots the discriminant of the quadratic equation must be equal to 0

☛ Discriminant, D = b² - 4ac = 0

☛ b² - 4ac = 0

☛ (-k)² - 4(2)(k) = 0

☛ k² - 8k = 0

☛ k(k - 8) = 0

k = 0 , k = 8

Here,

Value of k = 0, 8

Answer 2

The accurate answer is k = 0 or 8

Step-by-step explanation:

Given:

2x² - kx + k = 0 has equal roots.

To find:

The value of k

Solution:

We can solve by using Discriminat .

What is discriminat ?

The discriminant is the part of the quadratic equation in which the square root symbol: (coefficient of x)²- 4(coefficient of x²)(constant). The discriminant tells us whether there are two solutions, one solution, or no solutions.

When the quadratic equation have equal roots then the discriminant is equal to zero.

So,

Comparing the equation 2x² - kx + k = 0 from ax² + bx + c = 0 [where a ≠ 0] I get,

a = 2, b = - k, c = k

Now,

${b}^{2} - 4ac = 0 \\ \\ Or, \: {( - k)}^{2} - 4(2)(k) \\ \\ Or, \: {k}^{2} - 8k = 0 \\ \\ Or, \:k(k - 8) = 0 \\ \\ \text{Either,}\: k = 0 \\ \\ \text{Or,} \: \: \: k - 8 = 0 \: \implies \: k = 8$

$\therefore$ The required value of k is 8 or 0 when the equation have equal roots.