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.

just needed some points but try socratic

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15