Ask a New Question
Menu

the function with the sum of roots of 11 and product of roots is 11 is..?

thanks for the help!

User Icon for drwls drwls answered
14 years ago

Assuming the function is quadratic with an x^2 coefficient of 1,

in the form ax^2 + bx + c = 0.

x = [-b +/- sqrt(b^2 -4ac)]/2a

root sum = -b/a = -b
root product = (1/4a^2)*(-4ac) = -c

x^2 -11x -11 = 0 is the function

Roots are (1/2)(11 + sqrt165)
and (1/2)(11 - sqrt165)

There are many other functions that would meet your criteria, but all of the quadratic ones must be a multiple of the one above.

User Icon for Explain Bot Explain Bot answered
11 months ago

To find the function with the given conditions, we can use the fact that for a quadratic equation of the form ax^2 + bx + c = 0, the sum of the roots is given by -b/a, and the product of the roots is given by c/a.

Given that the sum of the roots is 11 and the product of the roots is also 11, we can set up the following equations:

- b/a = 11 (1)
c/a = 11 (2)

Since we have two equations with two variables (b and c), we can solve them simultaneously to find the values of b and c.

From equation (1), we can isolate b:
b = -11a (3)

Substituting equation (3) into equation (2), we get:
c/a = 11

Multiplying both sides by a, we get:
c = 11a (4)

Now we have expressions for b and c in terms of a. We can substitute these expressions into the general quadratic function: f(x) = ax^2 + bx + c.

Substituting b and c, we have:
f(x) = ax^2 - 11ax + 11a

Therefore, the function with the sum of roots of 11 and product of roots also 11 is f(x) = ax^2 - 11ax + 11a.

Note: The value of 'a' can be any non-zero real number since it does not affect the sum or product of the roots.