find two Integers if their product is - 8 and one integer is 6 less then the other
Answers
The two integers are 2 and -4
or
The two integers are 4 and -2
Explanation:
Given:
1. Two Integers if their product is - 8
2. One integer is 6 less than the other
To find:
The two Integers
According to condition1,
==> Let, Two Integers are x and y
==> Two Integers if their product is - 8
==> xy=-8 ==> 1
According to condition2,
==> x = x
==> y = x-6 ==>2
==> Substitute equation 2 in 1
==> x(x-6)=-8
==> x²-6x =-8
==> x²-6x +8 =0
==> This forms the quadratic equation
==> sum of zeros = -6
==> Product of zeros = 8
==> -4-2=6
==> (-4)(-2)=8
==> x²-4x-2x +8 =0
==> x(x-4)-2(x-4)=0
==> (x-2)(x-4)=0
==> x=2, x=4
We have two x values.
==> x=2
Substitute in the equation2
==> y = x-6
==> y = 2-6
==> y = -4
==> x=2 and y=-4
Substitute the values in the equation 1
==> xy=-8
==> (2)(-4)=-8
==> -8=-8
==> x=4
Substitute in the equation2
==> y = x-6
==> y = 4-6
==> y = -2
==> x=4 and y=-2
Substitute the values in the equation 1
==> xy=-8
==> (4)(-2)=-8
==> -8=-8
The two integers are 2 and -4
or
The two integers are 4 and -2