Range of k for Non-Real Roots: Solve x2 + (k - 2) x + (k + 3)

Thread starter Paulo2014
Start date Aug 24, 2008
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AI Thread Summary

To determine the range of values of k for which the roots of the equation x² + (k - 2)x + (k + 3) are not real, one must analyze the discriminant. The discriminant is given by D = (k - 2)² - 4(k + 3). For the roots to be non-real, the discriminant must be less than zero, leading to the inequality (k - 2)² - 4(k + 3) < 0. Solving this inequality will yield the specific range of k values. Understanding the discriminant is crucial for solving quadratic equations and determining the nature of their roots.

Aug 24, 2008

Paulo2014

Homework Statement

Find the range of values of k for which the roots of the equation
are not real.

Homework Equations

y = x2 + (k - 2) x + (k + 3)

The Attempt at a Solution

I have no idea...

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Aug 24, 2008

dirk_mec1

Look at the discriminant.

Aug 24, 2008

tiny-tim

Science Advisor

Homework Helper

dirk_mec1 said:

Look at the discriminant.

Or complete the square (same result, obviously)

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