What two numbers multiply to 24 and add to 1?

Answer 1

25

Answer 2

Let A,B be any number (in this case, the numbers won't be real)

A x B = 24

A + B = 1

Solve for A or B in either equation, and plug that value into the other equation.

A + B = 1

A = 1 - B

AB = 24

(1-B)B = 24

B - B2 - 24 = 0

(-1)(-B+B2+24)=0

B2-B+24=0 <--- you have a polynomial, which cannot be factored, so use the quadatric formula

B = (1±√(1-96))/2

B = 1/2 ± (√95)i/2

You can plug B back into either equation to find what A is, but in this case one number will the the positive 1/2 + (√95)i/2 and the other will be the negative 1/2 - (√95)i/2 version of the answer.

Check your work:

(1/2 + (√95)i/2)(1/2 - (√95)i/2) = 24

(1/2 + (√95)i/2) + (1/2 - (√95)i/2) = 1

The answer is:

(1/2 + (√95)i/2) and (1/2 - (√95)i/2)

Answer 3

NONE