Question 888877: Hi! We are asked to determine the nature of the roots of this problem:
x^2+5x=4
please indicate whether it is;
*Rational/Irrational
*Real/Non-Real
*Equal/Unequal
And kindly explain why you say so. Thanks!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x^2 + 5x = 4
subtract 4 from both sides to get:
x^2 + 5x - 4 = 0
now it's in standard form where:
a = coefficient of x^2 term = 1
b = coefficient of x term = 5
c = constant term = -4
the quadratic formula is:
x = (-b +/- sqrt(b^2-4ac)) / 2a
the discriminant is b^2 - 4ac.
the discriminant is what tells you where the roots are going to be rational or irrational or real or not real or equal or not equal.
in this problem, your discriminant becomes:
5^2 - 4*1*-4 = 25 + 16 = 41
since this is positive, then the roots are real.
since it is not a perfect square, the roots are irrational.
fyi - a perfect square is the square root of a number that is an integer.
for example:
16 is a perfect square because the square root of 16 = 4.
17 is not a perfect square because the squar root of 17 is not an integer.
here's a reference that should help you to understand what the discriminant is and what it tells you about the roots of the quadratic equation.
http://www.mathwarehouse.com/quadratic/discriminant-in-quadratic-equation.php
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