Find the roots of the equation by picking numbers that fit vieta’s theorem: x^2−19x+88=0

  roots are 8 and 11

Step-by-step explanation:

Vieta's theorem tells you the sum of roots in this case* is the opposite of the x-coefficient, so is 19. Their product is the constant term, 88.

It is convenient to search for the roots by considering the factors of 88:

  88 = 1·88 = 2·44 = 4·22 = 8·11

Only the latter pair of factors has a sum of 19, so those are the roots we're looking for.

The roots of the equation are 8 and 11.

* If the quadratic is ax²+bx+c with a≠1, then the sum of roots is -b/a, and their product is c/a.

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step-by-step explanation: