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

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

heavenwagner

17.03.2022

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:

$ax^2 + bx + c = 0, a \neq 0$

It will have no roots if:

$\Delta = b^2 - 4ac < 0$

In this question, we have that:

hx^2 + hx - 4 = 0

So, the coefficients are:

a = h, b = h, c = -4

Then

$\Delta < 0$

b^2 - 4ac < 0

h^2 - 16h < 0

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

The roots are:

h^2 - 16h = 0

h(h - 16) = 0

h = 0 or h = 16.

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

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