Question

What is the solution set of the quadratic inequality mc010-1.jpg
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Answer 1

I can solve that, but I can't see the image files you referenced. Please either paste the inequality text here (for example "x^2 − 5x + 6 < 0") or re-upload the images.

While you paste it, here’s the quick method I’ll use (so you know what to expect):

1. Put everything on one side so you have f(x) = ax^2 + bx + c compared to 0.
2. Find the discriminant D = b^2 − 4ac.
- If D < 0: f(x) has no real roots, so f(x) keeps the sign of a for all x (solution is all real x or no x depending on the inequality).
- If D = 0: a double root r = −b/(2a). Then f(x) = a(x − r)^2 so f(x) ≥ 0 if a > 0 and ≤ 0 if a < 0; strict inequalities give no solution, nonstrict include r.
- If D > 0: two real roots r1 < r2. Use a sign chart: for a > 0, f(x) > 0 for x < r1 or x > r2, and f(x) < 0 for r1 < x < r2. For a < 0 the signs are reversed.
3. Include endpoints if the inequality is ≤ or ≥.

If you paste the exact inequality I’ll solve it step by step and give the solution set.