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Write the discriminant of the following quadratic equations:

$x 2 − 2 x + k = 0, k ∈ R$

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8

4 2 − k

4 1 − k

4 k

answer is C.

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Detailed Solution

Given,

x 2 − 2 x + k = 0, k ∈ R

Calculate the discriminant by using the following formula,
D

= b 2 − 4 a c

[where a, b, c are the coefficients of the quadratic equation and

a ± 0

Therefore, from (1),

a = 1

b = - 2

c = k

Substitute the following values of a, b and c to calculate the discriminant for (1): Therefore,

D = b 2 − 4 a c ⇒ D = (− 2) 2 − (4 × 1 × k) ⇒ D = 4 − 4 k ⇒ D = 4 (1 − k)

Thus, it can be clearly concluded that the discriminant of the given quadratic equation is 4(1-k).
So, the correct option is 3.

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