Question

What multiply to 26 and add up to 7 ?

Answer 1

xy=26
x+y=7

if xy=26 then y=26/x

plugging this into our second equation we have

x+26/x=7

multiply both sides by x

x^2+26=7x

x^2-7x+26=0

use quadratic equation to find x

Answer 2

Make a table of all the factors (both positive and negative)



1 26
2 13
-1 -26
-2 -13


Now add up each pair


1+26 = 27
2+13 = 15
-1+(-26) = -27
-2+(-13) = -15



So there are no two rational numbers that multiply to 26 and add to 7

Answer 3

\[x=\frac{7 \pm \sqrt{(-7)^2-4(1)(26)}}{2(1)}=\frac{7 \pm \sqrt{49-104}}{2}\]
make that imaginary

Answer 4

a*b=26
a+b=7
b=26/a
a + 26/a = 7
a^2 + 26 = 7*a
a^2 - 7a + 26 = 0
7^2 - 4*26 = 49 - 104 < 0 so solutions will be complex. There are no real solutions.

Answer 5

we have to look at all complex numbers to answer this one

Answer 6

\[x=\frac{7 \pm \sqrt{-55}}{2}=\frac{7 \pm i \sqrt{55}}{2}\]

y=26/x
\[=\frac{26(2)}{7 \pm i \sqrt{55}}=\frac{52}{7 \pm i \sqrt{55}}\]

Answer 7

never mind i messed that wasn't even a problem i looked at 2 different problems and put it as 1 sorry lol

Answer 8

up*