Question

(1) If the roots of x2 + kx + k = 0 are real and equal, what is the value of k?
(A) 0
(B) 4 (C) 0 or 4
(D) 2​

Answer 1

Answer:

0 or 4

Step-by-step explanation:

To roots to be real and equal, discriminant of the equation must be 0.

Discriminant of ax² + bx + c = 0 is given by b² - 4ac.   On comparing,

a = 1,   b = k,     c = k

  ⇒ discriminant = 0

  ⇒ k² - 4(1)(k) = 0

  ⇒ k² - 4k = 0

  ⇒ k(k - 4) = 0

  ⇒ k = 0    or  k - 4 = 0

  ⇒ k = 0    or  k = 4

Answer 2

Answer:

Given :-

$\bf \: {x}^{2} + kx + k$

To Find :-

Value of k

Solution :-

Since there root are real and equal

D = b² - 4ac

[Discriminant Rule]

D = 0

b = k

a = 1

c = k

0 = k² - 4(1)(k)

0 = k² - 4k

0 = k(k - 4)

Either

$\sf \: k = 0 + 4$

$\sf \: k = 4$

Or

$\sf \: k = 0$