SOLUTION: Prove that the roots of 2x^2+8x+5 are real and irrational

Question 952164: Prove that the roots of 2x^2+8x+5 are real and irrational
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
look at the discriminant.
a = 2
b = 8
c = 5
b^2 - 4ac = 64 - 4*2*5 = 64 - 40 = 24
24 is positive and not a perfect square so the roots are real and irrational.
in order for the roots to be real and rational, the discriminant has to be positive and has to be a perfect square.
a perfect square is when the square root of a number is an integer.
sqrt(24) is not an integer.
but it is positive.

RELATED QUESTIONS
The roots of the equation 2x^2-5=0 are 1) imaginary 2) real, rational, and equal... (answered by edjones)

All the roots of x^2 + px + q = 0 are real, where p and q are real numbers. Prove that... (answered by ikleyn)

PRove that the roots of the given equation are real... (answered by ewatrrr)

The Discriminant Problem: The roots of the equation 2x2+6x+5=0 1]imaginary 2] real... (answered by ewatrrr)

prove that the roots of the quadratic equation are real when the discriminant is... (answered by richard1234)

1. Given the following polynomial: 2x^2 + 7x - 15 = 0 Check all that apply.  (answered by MathLover1)

I. Given the following polynomial: 2x^2+7x-15=0 . Check all that apply.  The (answered by josgarithmetic,MathTherapy)

Is the number 7 a discriminant of a quadratic equation whose roots are real, unequal, and (answered by stanbon)

Determine the nature of the solutions to the equation: 4x^2 = - 8x A. Two... (answered by josgarithmetic)