Question

The equation kx^2+2kx - 4 + k = 0 has no real
roots. Find the range of values of k.

Answer 1

Answer:

k belongs to [-2,+2]

Step-by-step explanation:

For real root of a quadratic equation ax^2 + bx + c=0

b^2 >= 4ac

here , x^2 -2kx + 2k^2 -4 =0

a = 1

b= -2k

c= 2k^2 -4

Now , putting these value in b^2 >= 4ac

we get ,

(-2k)^2 >= 4 (1) (2k^2 -4)

4k^2 >= 4(2k^2 -4)

k^2 >=2k^2 -4

-k^2 >= -4

k^2<=4

k<=+2,-2

therefore range of k , k belongs to [-2,+2]