Given that kx^2 + hx - 4 = 0 has no roots. Find the ranges of value of k

The ranges of value of k are values larger than 0 and lower than 16.

Step-by-step explanation:

Suppose we have a second order polynomial in the following format:

It will have no roots if:

In this question, we have that:

So, the coefficients are:

Then

A quadratic function, with a positive(as is 1 in this inequality), will be negative between it's roots.

The roots are:

So

h = 0 or h = 16.

The ranes of value of k are values larger than 0 and lower than 16.

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step-by-step explanation:

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