Question

Consider the polynomials p left parenthesis x right parenthesis equals 21 x minus 4 x squared and q left parenthesis x right parenthesis equals 5 . Find the x -coordinate(s) of the point(s) of intersection of these two polynomials. What is the sum of these x -coordinates

Answer 1

Answer:

  21/4 = 5.25

Step-by-step explanation:

You want the sum of the x-values that are solutions to ...

  21x -4x² = 5

  4x² -21x +5 = 0 . . . . . subtract the left side, rearrange to standard form

  x² -(21/4)x +5/4 = 0 . . . divide by 4

In this form the sum of the x-values that solve this equation is the opposite of the x-coefficient. That sum will be 21/4 = 5.25. (The attached graph confirms this result.)

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Consider a quadratic with roots p and q. It factors as ...

  (x -p)(x -q) = 0 = x² -(p+q)x +pq

That is, the x-coefficient is the opposite of the sum of the roots p and q.