In google type:
quadratic equation online
When you see list of result click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula
When page be open in rectangle type your equation
and cilck option:
You will see solutions step-by step and discriminant discusion.
I am only going to do one,
1. Use the discriminant to determine whether the given equation has two irrational roots, two rational roots, one repeated root, or two complex roots.
a.) Two rational roots
b.) one repreated root
c.) two complex roots
d.) two irrational roots.
Write with a zero on the right in form
a x^2 + b x + c = 0
1 x^2 -4 x - 5 = 0
b^2 = (-4)(-4) = 16
-4ac = -4(1)(-5) = +20
b^2 -4ac = 16+20 = 36
sqrt (b^2 - 4ac) = +6
x = [ 4 +/- 6 ] /2
Two REAL Rational roots
sqrt (+36) is a real number
sqrt (+36) is not sqrt( 0) which would give one repeated root
sqrt(+36) is not sqrt(-36) which would leave you with a +/- 6i which is COMPLEX number
it is not sqrt (2) or something which is not a nice rational number and can not be expressed as a ratio of whole numebers
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