two numbbers have sum of 9 and product of 20. What singlevariable quadratic equation in form of ax^2+bx+c=0 can be used to represent the product of the two numbers
let the two numbers be x and y
so we have:
x+y = 9 --->y = 9-x
and
xy = 20
x(9-x) = 20
9x - x^2 - 20 = 0
the equation you want is:
x^2 - 9x + 20 = 0
easily solved, it even factors nicely.
To find a quadratic equation that represents the product of two numbers, let's assume the two numbers are x and y.
From the given information, we know that the sum of the two numbers is 9, so we can write the equation:
x + y = 9 -- Equation 1
We also know that the product of the two numbers is 20, so we can write the equation:
xy = 20 -- Equation 2
To find a quadratic equation, we want to express one variable in terms of the other and substitute it into Equation 2. Let's solve Equation 1 for one of the variables:
x + y = 9
y = 9 - x
Now, substituting y in Equation 2:
x(9 - x) = 20
Expanding and rearranging:
9x - x^2 = 20
Rearranging to the standard form of a quadratic equation:
x^2 - 9x + 20 = 0
So the single-variable quadratic equation that represents the product of the two numbers, given their sum of 9 and product of 20, is:
x^2 - 9x + 20 = 0