Question

If -4 is a root of the quadratic equation x2+px-4=0 and the quadratic equation x2+px+k=0 has equal roots, find the value of k.

Answer 1

Answer:

k= 9/4

(p =3)

Step-by-step explanation:

1st quadratic equation:

x² + px -4=0

put x=-4

(-4)² +(-4)p -4 = 0

16 -4p -4 = 0

12 -4p =0

(shift 12 to RHS)

-4p = -12

p = -12/-4

p=12/4

p= 3 -------->(1)

2nd quadratic equation :

x² +px +k = 0

put p=3

x² + 3x + k = 0 (from (1))

comparing with,

ax²+bx+c=0

we get,

a=1

b=3

c=k

since, the equation has equal roots

thus,

delta=0

b²-4ac=0

3²-4×1×k=0

9- 4k = 0

-4k = -9

k = -9/-4

k=9/4

hope this helps you..