A quadratic equation in standard form that can be used to determine the value of x is [tex]x^{2}[/tex] - 8x - 65 = 0.
The Factor of the equation from Part B is (x - 13)(x + 5) and the possible solutions to the equation is x = 13 or -5.
The value for the second number is 5
The general formula for quadratic equation in a in standard form is
a[tex]x^{2}[/tex] + bx + c = 0
Given that the difference between two integers is 8
Let the two integers = x and y,
and their product is 65. If the larger of the two numbers is x. Then,
x - y = 8 and xy = 65
Since we are looking for the value of x, make y the subject of formula in the first equation.
y = x - 8
Substitute y in the second equation.
x(x - 8) = 65
[tex]x^{2}[/tex] - 8x - 65 = 0
[tex]x^{2}[/tex] - 13x + 5x - 65 = 0
(x - 13)(x + 5) = 0
x = 13 or -5
We will ignore -5 since x is the larger number.
To get y Substitute x in the second equation.
xy = 65
13y = 65
y = 65/13
y = 5
Therefore, a quadratic equation in standard form that can be used to determine the value of x is [tex]x^{2}[/tex] - 8x - 65 = 0. The Factor of the equation from Part B is (x - 13)(x + 5) and the possible solutions to the equation is x = 13 or -5. The value for the second number is 5
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