Question 84093
You're supposed to find the roots of the equations. Since the
largest exponent is 2 (x^2), there are 2 roots in each case.
The roots are values for the unknown that make the equation 0.
Say the roots are r1 and r2, then
(x - r1)(x - r2) = 0
If you then make x = r1,
(r1 - r1)(r1 - r2) = 0 this is true
If you make x = r2, then
(r2 - r1)(r2 - r2) = 0 this is true also
How do you find the roots? Use the so-called quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a = 14
b = -20
c = +6
{{{x = (-(-20) +- sqrt( (-20)^2-4*14*6 ))/(2*14) }}}
{{{x = (20 +- sqrt(400 - 336))/28 }}}
{{{x = (20 +- sqrt(64))/28 }}}
{{{x = (20 + 8) / 28}}}
and
{{{x = (20 - 8) / 28}}}
or, {{{x = 1}}} and {{{x = 3/7}}}
So, your factors are
{{{(x - 1)(x - (3/7))}}}
Do these multiplied together give you the original equation?
{{{(x - 1)(x - (3/7)) = x^2 -(10/7)x + 3/7}}}
Multiplying both sides by 14,
{{{14*(x - 1)(x - (3/7)) = 14x^2 - 20x + 6}}}
So, 1 and 3/7 are the factors.
The other equation is factored in the same manner