Question

Can someone please check my work on this math question? please? I'll fan and give a medal!!

Answer 1

The product of two consecutive odd integers is 63. Write a quadratic equation that you could solve to find the integers, then find the integers.

Answer 2

@JianEnriquez could you please try to help me?

Answer 3

Let n be the first integer. The next integer after that is n+1. Since we want 2 odd integers, this means we need to jump to n+2

example: say n = 3, the next is n+1 = 4 and the next after that is n+2 = 5
So we're focused on n = 3 and n+2 = 5

In general, we have n and n+2 as our two unknown numbers. They multiply to get 63, so,

(first number)*(second number) = 63
(n)*(n+2) = 63
n^2+2n = 63

Do you see what to do next?

Answer 4

(3)*(21+2) = 63 ?

Answer 5

why not subtract 63 from both sides?

n^2+2n = 63
n^2+2n-63 = 63-63
n^2+2n-63 = 0

Then use the quadratic formula

Answer 6

Or you could factor, but factoring won't always work with quadratics. The quadratic formula always works with any quadratic.

Answer 7

oh okay so I just factored it and got (n−7)(n+9)

Answer 8

good, so set that equal to zero and use the zero product property to solve for n

(n-7)*(n+9) = 0

n-7 = 0 ... or ... n+9 = 0

n = ?? ... or ... n = ???

Answer 9

n=7 or n=−9 ?

Answer 10

yes

Answer 11

n = 7
n+2 = 7+2 = 9

so the two numbers are 7 and 9

7*9 = 63

--------------------------

n = -9
n+2 = -9+2 = -7

or you could say the two numbers are -9 and -7
-9*(-7) = 63

Answer 12

thank you very much!!! you're awesome!!

Answer 13

glad to be of help