Question 924080
{{{ x = -4 }}}
{{{ x = 3 }}}
are solutions
{{{ 5x^2 + b*x + c = 0 }}}
The solutions are:
(1) {{{ 5*(-4)^2 + b*(-4) + c = 0 }}}
and
(2) {{{ 5*3^2 + b*3 + c = 0 }}}
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(1) {{{ 80 - 4b + c = 0 }}}
(2) {{{ 45 + 3b + c = 0 }}}
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Subtract (2) from (1)
(1) {{{ 80 - 4b + c = 0 }}}
(2) {{{ -45 - 3b - c = 0 }}}
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{{{ 35 - 7b = 0 }}}
{{{ 7b = 35 }}}
{{{ b = 5 }}}
and
(1) {{{ 80 - 4*5 + c = 0 }}}
(1) {{{ 80 - 20 + c = 0 }}}
(1) {{{ c = -60 }}}
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The equation is:
{{{ f(x) = 5x^2 + 5b - 60 }}}
check:
{{{ ( x - 3 )*( x + 4 ) = 0 }}}
{{{ x^2 - 3x + 4x - 12 = 0 }}}
{{{ x^2 + x - 12 = 0 }}}
Multiply both sides by {{{ 5 }}}
{{{ 5x^2 + 5x - 60 = 0 }}}
OK