Question

Describe the nature of the roots for this equation.

x^2+3x-7=0

A. Two real, rational roots
B. Two real, irrational roots
C. Two complex roots
D. One real, double root

Answer 1

in an equation like
\[ ax^2+bx+c=0 \]
the solutions are given by
\[ \LARGE x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \]
depending on the value of
\[ \Delta=b^2-4ac \]
you have either
(i) two real roots
(ii) one (repeated) real root
(iii) two complex roots

Answer 2

use b^2 - 4ac 3^2 - 4*1*-7 = 33

then there are 2 unequal irrational roots