Question 1149382
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{{{f(x) = ax^2+bx+c}}}<br>
Use the remainder theorem:<br>
{{{f(x)/(x-1) = -6}}} --> {{{f(1) = -6}}} --> {{{a+b+c = -6}}} (1)<br>
{{{f(x)/(x-3) = -4}}} --> {{{f(3) = -4}}} --> {{{9a+3b+c = -4}}} (2)<br>
{{{f(x)/(x+1) = 0}}} --> {{{f(-1) = 0}}} --> {{{a-b+c = 0}}} (3)<br>
That gives you 3 equations in 3 unknowns; solve by any method you like.<br>
A good start might be subtracting (3) from (1); that eliminates both a and c, giving you an equation that is easily solved to find the value of b.<br>
Then substitute that value of b in (1) and (2) and solve the resulting pair of equations for a and c.<br>