Question

Which two numbers add up to 5 and multiply to -45 ?

Answer 1

We have x+y=5
xy=-45
solve
x+y=5
subtract x from both sides
y=-x+5
subsiute -x+5 for y in second equaiton
x(-x+5)=-45
-x^2+5x=-45
add 2x^2-5x to both sides
0=x^2-5x-45
use quadratic equation which is
if you have 0=ax^2+bx+c then x=$\frac{-b+ \sqrt{b^{2}-4ac} }{2a}$ or $\frac{-b- \sqrt{b^{2}-4ac} }{2a}$
sbsitute
1x^2-5x-45
a=1
b=-5
c=-45
subsitute
$\frac{-(-5)+ \sqrt{-5^{2}-4(1)(-45)} }{2(1)}$
$\frac{5+ \sqrt{25-(-180)} }{2}$
$\frac{5+ \sqrt{25+180} }{2}$
$\frac{5+ \sqrt{205} }{2}$
$\sqrt{205} [tex} is not eaqual to a whole number so we will leave it like that\\x= [tex] \frac{5+ \sqrt{205} }{2}$ or$\frac{5- \sqrt{} }{2}$ or aprox x=-4.65891 or 9.65891, so the 2 numbers would be those answers for x