If (x-6) is a factor of x^3-ax^2+bx-6=0 and ( a-b=7) find the value of a and b.
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x-6 is a factor of given equation, therefore f(6)=0;
substituting values,
6³-a(6²)+b(6)-6=0
216-36a+6b-6=0
-36a+6b+210=0
dividing both sides by 6
-6a+b+35=0
and a-b=7 is given; solving simultaneously, we get 7a=-28; a=-4
so b=11
substituting values,
6³-a(6²)+b(6)-6=0
216-36a+6b-6=0
-36a+6b+210=0
dividing both sides by 6
-6a+b+35=0
and a-b=7 is given; solving simultaneously, we get 7a=-28; a=-4
so b=11
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