Hi, I need help doing these two. Can someone explain. Medal

How many real number solutions does the equations have?

0 = 5x^2 + 2x - 12
0 = 2x^2 - 20x + 50

Question

Hi, I need help doing these two. Can someone explain. Medal

How many real number solutions does the equations have?

0 = 5x^2 + 2x - 12
0 = 2x^2 - 20x + 50

campbell_st · Answer

do you know about the discriminant 

$$\Delta = b^2 - 4ac$$

dtan5457 · Answer

Yup ^, all you need is the discriminant.

If it equals 0, it's two equal real solutions.

<0, 2 imaginary solutions

>0, rational or irrational, equal or unequal depending if it's a perfect square

romantic_ch3micals · Answer

So they both have two equal solutions because they equal 0? @dtan5457

dtan5457 · Answer

My bad, if it's equal to 0, there is one real solution.

romantic_ch3micals · Answer

Oh, well, I get that but is there something else I should know? I really want to get this.

campbell_st · Answer

= 0 its 1 repeated real solution

romantic_ch3micals · Answer

Ok, so they both have one solution because it equals to 0. Am I correct?

dtan5457 · Answer

Are you referring to your questions?

romantic_ch3micals · Answer

Yeah.

dtan5457 · Answer

You need to use the discriminant of b^2-4ac to figure that out.

Just because the quadratic=0, doesn't mean the discriminant is 0.

dtan5457 · Answer

I'll do the first one.

0 = 5x^2 + 2x - 12

B^2-4ac

value of b=2
value of a=5
value of c=-12

(2)^2-4(5)(-12)=244

244 is not a perfect square.

therefore it has 2 unequal, irrational real solutions.

try the second one.

romantic_ch3micals · Answer

Ok.
 eh, Ive work it out on paper and I got three...is that right? @dtan5457