How would you factor y = -3x2 - 18x -20? With your answer, what would your x values be when y = 0? Show your steps. Explain why your x values have 2 answers.

Question

How would you factor y = -3x² - 18x -20? With your answer, what would your x values be when y = 0? Show your steps. Explain why your x values have 2 answers.

Answer 1

If you solve using the quadratic formula the factors are (x- each root) so in this case roots are

 

x=-3 -/+ sqrt(21)/3

 

(x-(-3 - sqrt(21)/3))(x-(-3 + sqrt(21)/3))   factored

 

2 roots because discriminant is non-zero

Answer 2

y = -3x² - 18x -20 = -(3x² + 18x + 20) is not factorable. The discriminant D = 18²=4(3)(20)=324-240=84. since 84 is not a perfect square, both roots are irrational.

The zeros are given by the quadratic formula: [-18√84]/6.

 

There are two zeros (roots, a.k.a. x-intercepts) because it's a quadratic equation when you set y=0).

 

Had the discriminant been zero, there would be only one so-called double root (rational). Had D been < 0, there'd be no Real roots.