SOLUTION: Determine the number of solutions and classify the type of solutions for each equation. Justify the answer. x^2+3x-15=0 x^2x+4=0 x^2-8x+16=0 2x^2-3x+7=0

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Determine the number of solutions and classify the type of solutions for each equation. Justify the answer. x^2+3x-15=0 x^2x+4=0 x^2-8x+16=0 2x^2-3x+7=0      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 199156: Determine the number of solutions and classify the type of solutions for each equation. Justify the answer.
x^2+3x-15=0
x^2x+4=0
x^2-8x+16=0
2x^2-3x+7=0

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Each of these problems is in the form:



For each of them, calculate the discriminant ():



Then evaluate the character of the roots based on the value of according to the following criteria (which presume rational coefficients on your quadratic):

Two real and unequal roots. If is a perfect square, then both roots are rational. Otherwise the two roots are a conjugate pair of irrational roots of the form where is rational and is irrational.

One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors.

A conjugate pair of complex roots of the form where is the imaginary number defined by

John