Lesson 15 Summary
You can use the sign of the discriminant, b2 - 4ac, to determine the number of real solutions to a quadratic equation in the form ax2 + bx + c = 0, where a ≠ 0.
If the equation has a positive discriminant, there are two real solutions.
A negative discriminant yields no real solutions and a discriminant equal to zero yields only one real solution.
Solve the following equations using the quadratic formula.
1. x2 - 2x + 1 = 0
2. 3b2 + 4b + 8 = 0
3. 2t2 + 7t - 4 = 0
4. q2 - 2q - 1 = 0
5. m2 - 4 = 3
For Exercises 6–9, without solving, determine the number of real solutions for each quadratic equation.
6. p2 + 7p + 33 = 8 - 3p
7. 7x2 + 2x + 5 = 0
8. 2y2 + 10y = y2 + 4y - 3
9. 4z2 + 9 = -4z
10. State whether the discriminant of each quadratic equation is positive, negative, or equal to zero on the line below the graph. Then identify which graph matches the discriminants below:
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