Answer:
1295/36
Step-by-step explanation:
the statement tell us:
(7-(5/6))*(7-(7/6))
we have:
(7-(5/6))=((6*7)-5)/6=(42-5)/6=37/6
and we have:
(7-(7/6))=((6*7)-7)/6=(42-7)/6=35/6
we need multiply both terms:
(37/6)*(35/6)=(37*35)/(6*6)
finally we have
1295/36
Step-by-step explanation:
they're is a neat little trick.
but first of all, "roots" means the 0 solutions of the equation. like
ax² + bx + c = 0
there are 2 solutions for x to make the whole expression equal 0.
these are the "roots".
now to the little trick :
when is a multiplication resulting in 0 ?
when at least one of the factors is 0.
and any quadratic expression can be written as multiplication of 2 factors. like
c(x - a)(x - b) = cx² - cax - cbx + cab
what are the "roots" or 0 points ?
either
c = 0
x - a = 0 | x = a
x - b = 0 | x = b
the leading coefficient = 3.
that means nothing else than c = 3.
root = 1 means (x - 1) is one factor.
root = -5 means (x + 5) is the other factor.
so, we have
3(x - 1)(x + 5) = 3x² + 12x - 15
and the equation is
3x² + 12x - 15 = 0
or
3x² + 12x = 15
