SOLUTION: Given 2x^2+bx+8, find the values of b so there are no real solutions to the quadratic.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Given 2x^2+bx+8, find the values of b so there are no real solutions to the quadratic.      Log On


   

Question 1002188: Given 2x^2+bx+8, find the values of b so there are no real solutions to the quadratic.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Given 2x%5E2%2Bbx%2B8, find the values of b so there are no real solutions to the quadratic
use discriminant b%5E2-4ac
recall:
b%5E2-4ac%3E0 =>two real solutions
b%5E2-4ac=0 =>one (repeated) real solution
b%5E2-4ac%3C0=>two complex solutions
so you need b that will make b%5E2-4ac%3C0
in your case 2x%5E2%2Bbx%2B8, a=2,b=b,c=8
so,b%5E2-4%2A2%2A8%3C0
b%5E2-64%3C0
b%5E2%3C64
b%3Csqrt%2864%29
b%3C8
let's check if b=7
2x%5E2%2B7x%2B8=0
x+=+%28-7+%2B-+sqrt%28+7%5E2-4%2A2%2A8+%29%29%2F%282%2A2%29+
x+=+%28-7+%2B-+sqrt%28+49-64+%29%29%2F4+
x+=+%28-7+%2B-+sqrt%28+-15+%29%29%2F4+
x+=+%28-7+%2B-+i%2Asqrt%28+15+%29%29%2F4+->no real solutions,we have two complex solutions

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x%5E2%2B7x%2B8%29+