Question

I need help desperately! Could someone explain this math concept for me please?

Answer 1

The inequality that represents the range of k so that inequality 1 has real solution is -3 < k < 5

How to determine the range?

Inequality 1

x^2 + (k + 1)x + k + 4 > 0

The discriminant is calculated using

D = b^2 - 4ac

So, we have:

D = (k + 1)^2 - 4 * 1 * (k + 4)

Evaluate

D = k^2 + 2k + 1 - 4k - 16

This gives

D = k^2- 2k - 15

Factorize the equation

D = (k+ 3)(k -5)

Solve for k

k = -3 and k = 5

Express the k values as inequalities

-3 < k < 5

Inequality 2

The inequality cannot be read, because of the image quality

Read more about discriminant at:

brainly.com/question/7784687

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