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

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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.
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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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Look at the discriminant.
 
dirk_mec1 said:
Look at the discriminant.

Or complete the square (same result, obviously) :smile:
 

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