SOLUTION: Find the number and type of solutions for: 3x2 – 10x + 3 = 0.

Algebra ->  Inequalities -> SOLUTION: Find the number and type of solutions for: 3x2 – 10x + 3 = 0.      Log On


   

Question 1104519: Find the number and type of solutions for: 3x2 – 10x + 3 = 0.
Found 3 solutions by Alan3354, Shin123, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the number and type of solutions for: 3x2 – 10x + 3 = 0.
----
Use ^ (Shift 6) for exponents.
3x^2 – 10x + 3 = 0
----------
It's a quadratic, 2nd order. All quadratics have 2 solutions.
---
Find the discriminant, b^2 - 4ac
------------
Disc < 0 --> 2 complex solutions
Disc = 0 --> 2 equal real solutions.
Disc > 0 --> 2 unequal real solutions.

Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Use ^ for powers.
3x%5E2-10x%2B3=0 Use the quadratic formula,
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
x=%28-%28-10%29%2B-sqrt%28-10%5E2-4%289%29%29%29%2F2%283%29
x=%2810%2B-sqrt%28100-36%29%29%2F6
x=%2810%2B-sqrt%2864%29%29%2F6
x=%2810%2B-+8%29%2F6
system%28x=18%2F6=3%2Cx=2%2F6=1%2F3%29

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


If the question in fact only asks for the number and type of solutions, then all you need to do is look at the discriminant, b^2-4ac.

b%5E2-4ac+=+%28-10%29%5E2-4%283%29%283%29+=+100-36+=+64

The discriminant is positive; there are 2 real solutions.

Note the discriminant is a perfect square; that means the equation can be solved by factoring. Many students go straight to the quadratic formula every time for solving quadratic equations; however, with a little practice solving by factoring is faster.