Create a radical equation. Use a random number generator to generate TWO numbers

Question

Create a radical equation.

Use a random number generator to generate TWO numbers between -10 and 10 (they CANNOT be the same number).

Call these numbers A and B.

Use those numbers to create a polynomial (x-A)(x-B), expand this polynomial to the form ax^2 + bx + c

Use a random number generator AGAIN to get one number between -10 and 10 (that is different from A and B).

Call this number C.

Now write (x-A)(x-B) in the form (x-C)^2 + mx + b (where "m" and "b" are whatever is needed so that collecting like terms gets you back to (x-A)(x-B)).

Setting that expression equal to 0 and subtracting the mx+b to the other side, you are now ready to take the square root of both sides, and that creates a radical equation.

(2) Solve the radical equation you made. Are A and B both solutions, or is one of them a false/extraneous solution?

Explanation / Answer

let two numbers A and B be 2 and 3

( x- 2) ( x- 3) = x^2 - 5x + 6

from random number let another number be 4

C = 4

x^2 - 5x + 6 = ( x- 4 )^2 + 3x - 16

setting this expression to 0

( x- 4 )^2 + 3x+6 - 16 = 0

( x- 4)^2 + 3x - 10 = 0

( x- 4)^2 = 10 - 3x

taking square root on both sides

x - 4 = +- sqrt ( 10 - 3x )

yes both A and B are solutions of the radical equation

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