If the discriminant is greater than zero, how many real solutions does ax^2 + bx + c = 0 have?

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Study for the Algebra 1 Honors End-of-Course Test. Study with flashcards and multiple-choice questions, each question has hints and explanations. Get ready for your exam!

Multiple Choice

If the discriminant is greater than zero, how many real solutions does ax^2 + bx + c = 0 have?

Explanation:
The number of real solutions to a quadratic is determined by the discriminant Δ = b^2 − 4ac. When Δ is greater than zero, the parabola crosses the x-axis in two distinct places, so there are two real solutions. If Δ were zero, there would be one real solution (a repeated root), and if Δ were negative, there would be no real solutions (the roots would be complex). So with Δ > 0, you indeed get two real solutions. For example, x^2 − 5x + 6 = 0 has Δ = 25 − 24 = 1 > 0, giving roots x = 2 and x = 3. (Remember a ≠ 0 for a quadratic.)

The number of real solutions to a quadratic is determined by the discriminant Δ = b^2 − 4ac. When Δ is greater than zero, the parabola crosses the x-axis in two distinct places, so there are two real solutions. If Δ were zero, there would be one real solution (a repeated root), and if Δ were negative, there would be no real solutions (the roots would be complex). So with Δ > 0, you indeed get two real solutions. For example, x^2 − 5x + 6 = 0 has Δ = 25 − 24 = 1 > 0, giving roots x = 2 and x = 3. (Remember a ≠ 0 for a quadratic.)

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