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.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions