Question

Use the discriminant to determine the nature of the roots of the following equation.

y^2 - 5y - 3 = 0

Double root
real and rational root
real and irrational root
non-real root

Use the discriminant to determine the nature of the roots of the following equation.

x^2 + 2x + 5 = 0

Double root
real and rational root
real and irrational root
non-real root

Answer 1

\[discriminant=b^{2}-4ac\]
this is taken from the quadratic formula

if the discriminant >0 then it has two distinct roots
if the discriminant = 0 then it has a repeated root
if the disciiminant is < 0 then it has no real roots

rational number is a number that can be written as a ratio of integers (whole numbers) and not a decimal for example
2 is a rational number as 2/1 =2 and top and bottom of the fraction are both whole numbers

Answer 2

if it is still not clear then let me point out that
a= coefficient of the squared term
b= coefficient of the term to the power of 1
c= the constant

Answer 3

Thanks