Equation problem

[Loki123]

Plug in a=-7 and a=20. How many roots do you get?

1 each?

 

[BigBeachBanana]

1 each?

How? You'll always get 3 roots, but for a=-7 and a=20, you have repeated roots.
e.g.
$$3x^{2}+2x^{3}-12x+7=(x-1)^2(2x+7)=0\\ \implies x=-\frac{7}{2}\,\text{and }x=1 \text{ (repeated roots)}$$

 

[Loki123]

How? You'll always get 3 roots, but for a=-7 and a=20, you have repeated roots.
e.g.
$$3x^{2}+2x^{3}-12x+7=(x-1)^2(2x+7)=0\\ \implies x=-\frac{7}{2}\,\text{and }x=1 \text{ (repeated roots)}$$

so they don't we include -7 and 20

 

[BigBeachBanana]

so they don't we include -7 and 20

The question asked for distinct roots, didn't it?

 

[Loki123]

The question asked for distinct roots, didn't it?

oooh i get it now! thanks!