If – 4 is a root of the quadratic equation x2 + px – 4 = 0 and x2 + px + k = 0 has equal roots, find the value of k.
Answers
P(x) = x2 + px - 4
P (-4) = 16 -4p -4 =0
p = 3
for equal roots
b2 - 4ac =0
9 - 8k = 0
-8k = -9
k = 9/8
Hope it helps!!
Answer:
The value of p = 3 and k = 9/4
Given problem:
If – 4 is a root of the quadratic equation x² + px – 4 = 0 and x² + px + k = 0 has equal roots, find the value of k.
Step-by-step explanation:
Given quadratic equations f(x) = x² +px - 4 = 0_(1)
g(x) = x² +px +k = 0_(2)
root of equation (1) = - 4
then f(-4) = 0
⇒ (-4)² + p(-4) – 4 = 0
16 - 4p - 4 = 0
12 - 4p = 0
4p = 12
p = 3
p = 3 substitute in equation (2)
⇒ g(x) = x² +3x +k = 0
[ compare g(x) with ax²+bx +c = 0 ; a = 1, b = 3 and c = k ]
from given data g(x) has equal roots
⇒ discriminant D = b² - 4ac = 0
(3)² - 4(1)(k) = 0
9 - 4k = 0
4k = 9
k = 9/4