Question 336099
Find the value of a if:
{{{g(x) = K(x+3)(x-3)}}} K = some constant. and if...
{{{g(a-1.2) = 0}}} and {{{a>0}}}
In the given function {{{g(x) = K(x+3)(x-3)}}} simplify.
{{{g(x) = K(x^2-9)}}} For every x, replace with (a-1.2)
{{{g(a-1.2) = K((a-1.2)^2-9))}}} Expand the right side.
{{{g(a-1.2) = K((a^2-2.4a+1.44)-9)}}}
{{{g(a-1.2) = K(a^2-2.4a-7.56)}}} Now set this equal to zero since:{{{g(a-1.2)=0}}}
{{{K(a^2-2.4a-7.56) = 0}}} Apply the zero product rule:
{{{K = 0}}} or {{{a^2-2.4a-7.96 = 0}}}
{{{a^2-2.4a-7.56 = 0}}} You can use the quadratic formula to solve this and you should get:
{{{a = 4.2}}} or {{{a = -1.8}}}