We are given that:
Find the equation with roots and
The method which you have to do it in is the simplest method where u=?.
We are NOT allowed to use a brute force method
Can anyone please help?
Hello, anthmoo!
We are given that: .
Find the equation with roots and
I assume that and are the roots of the given equation.
The roots of the quadratic are: .
Let
Let
Then: .
. . This is the negative of the x-coefficient.
And: .
. . This is the constant term.
Therefore, the equation is: .
Thankyou Soroban but it says that I am not allowed to know or work out the roots of the equation. I am only supposed to work it out without knowing the roots.
In another question, it was asked
The equation has roots . By not using a brute force method, find the equations with roots
I completed this one successfully by using this method simply (the one i need to use):
This gives me the new equation:
which is the new equation
Although you got the right answer Soroban, I was strictly not allowed to use such a method! Can you get the same answer using my method?
Hello again, anthmoo!
I was afraid that used Brute Force . . . I'll try again.
We are given that:
Find the equation with roots and
Since and are roots of the quadratic,
. . we know that: . and
The roots of the new equation are: . and
The x-coefficient of the new equation is:
. .
Since , then: .
. . Hence, the x-coefficient is:
The constant term of the new equation is:
. .
. . . . .
. . . . .
. . . . .
. . . . .
Since and , then: .
. . Hence, the constant term is
Therefore, the equation is: .