Using the discriminant Δ=b2−4ac to determine the number of real roots, Vieta's formulas α+β=−ab
The discriminant of a quadratic is the term under the square root in the quadratic formula:
When Δ<0, the square root has a negative value inside, and so the quadratic has no real solutions.
When Δ=0, the square root is zero, and the ±√Δ makes no difference, so there is only one real solution.
When Δ>0, √Δ is positive and so ±√Δ yields two real roots.
In a quadratic ax2+bx+c, the roots α and β satisfy
Nice work completing Applications of Quadratics, here's a quick recap of what we covered:
Exercises checked off
Using the discriminant Δ=b2−4ac to determine the number of real roots, Vieta's formulas α+β=−ab
The discriminant of a quadratic is the term under the square root in the quadratic formula:
When Δ<0, the square root has a negative value inside, and so the quadratic has no real solutions.
When Δ=0, the square root is zero, and the ±√Δ makes no difference, so there is only one real solution.
When Δ>0, √Δ is positive and so ±√Δ yields two real roots.
In a quadratic ax2+bx+c, the roots α and β satisfy
Nice work completing Applications of Quadratics, here's a quick recap of what we covered:
Exercises checked off