Question

Write a quadratic equation where it can not be solved by factoring, but can still be solved by using the quadratic formila

Answer 1

I assume that the solutions have to be real

Answer 2

in which case, you need a quadratic equation with 2 irrational solutions

Answer 3

An example of this would be:
\[x^2 + 3x + 1\]

Answer 4

no rational numbers add up to 3 and multiply to equal one

Answer 5

therefore the solution must be either an irrational number or a imaginary number

Answer 6

if you take the discriminate:
\[b^2 - 4ac\]
you get 5

Answer 7

5 is positive, so the answer is real, however it is not a perfect square, so the answer is irrational.

Answer 8

Thank you so much