Question

the product of two consecutive integers is 90. Find the two integers then check your answer​

Answer 1

Answer:

9,10 or -10,-9

Step-by-step explanation:

Let call the first integer n and the second integer n+1 since they are consecutive.

Since the product of the integer is 90 set up this equation

$n \times (n + 1)= 90$

$n {}^{2} + n = 90$

Subtract 90 to get it on the left side

$n {}^{2} + n - 90$

Apply quadratic formula

$- 1 + - \sqrt{ \frac{1 {}^{2} - 4(1)( - 90) }{2(1)} }$

$- 1 + - \sqrt{ \frac{1 - ( - 360}{2} }$

$- 1 + - \sqrt{ \frac{1 + 360 = 361}{2} }$

$- 1 + - \frac{ \sqrt{361 = } 19}{2}$

The roots are n= -10 and 9. We can use either root but let use a positve root

We are taking the positve roots

Plug 9 as n into n+1

$9 + 1 = 10$

or

$- 10 + 1 = - 9$