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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In summary, the range of k for non-real roots in the equation x2 + (k - 2) x + (k + 3) is when k falls within the range of k < 2 - 2√6 or k > 2 + 2√6. The roots of this equation can be real or non-real, depending on the value of the discriminant. The equation can be solved using the quadratic formula, but the resulting roots may be non-real for certain values of k. To determine the range of k for non-real roots, the equation can be graphed and the range will be the values of k that do not intersect the x-axis.

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)

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

1. What is the range of k for non-real roots in the equation x2 + (k - 2) x + (k + 3)?

The range of k for non-real roots is when the discriminant, b2 - 4ac, is negative. In this equation, the discriminant is (k - 2)2 - 4(k + 3), which simplifies to k2 - 8k - 20. To find the range, we can set this expression less than 0 and solve for k. The range is k < 2 - 2√6 or k > 2 + 2√6.

2. How do I know if the roots of x2 + (k - 2) x + (k + 3) are real or non-real?

The roots of a quadratic equation can be real or non-real, depending on the value of the discriminant. If the discriminant is positive, the roots are real. If the discriminant is negative, the roots are non-real.

3. Is there a specific value for k that will always result in non-real roots?

Yes, when the value of k falls within the range of k < 2 - 2√6 or k > 2 + 2√6, the equation will always have non-real roots. However, it is important to note that this equation can also have non-real roots for other values of k, depending on the values of a, b, and c.

4. Can I use the quadratic formula to solve for the roots of x2 + (k - 2) x + (k + 3)?

Yes, you can use the quadratic formula, which is x = (-b ± √(b2 - 4ac)) / 2a, to solve for the roots of this equation. However, depending on the values of k, a, b, and c, the resulting roots may be non-real numbers.

5. How can I graph the equation x2 + (k - 2) x + (k + 3) to determine the range of k for non-real roots?

To graph this equation and determine the range of k for non-real roots, you can use a graphing calculator or software, or you can manually plot points and draw a graph. The range of k for non-real roots will be the values of k that fall above or below the x-axis, as the graph will not intersect the x-axis for these values.