Asked by Joey
Find a 4 degree polynomial having zeros -6,-3,2 and 6 and the coefficient of x^4 equal 1
The "coefficient of x^4 equal 1" is really throwing me off.
Thanks.
The "coefficient of x^4 equal 1" is really throwing me off.
Thanks.
Answers
Answered by
Bosnian
a x ^ 4 + b x ^ 3 + c x ^ 2 + d x + e =
a ( x - x1 ) * ( x - x2 ) * ( x - x3 ) * ( x - x4 )
In your case:
a = 1
So:
x ^ 4 + b x ^ 3 + c x ^ 2 + d x + e =
( x - ( - 6 ) ) * ( x - ( - 3 ) ) * ( x - 2 ) * ( x - 6 ) =
( x + 6 ) * ( x + 3 ) * ( x - 2 ) * ( x - 6 ) =
x ^ 4 + x ^ 3 - 42 x ^ 2 -36 x + 216
a ( x - x1 ) * ( x - x2 ) * ( x - x3 ) * ( x - x4 )
In your case:
a = 1
So:
x ^ 4 + b x ^ 3 + c x ^ 2 + d x + e =
( x - ( - 6 ) ) * ( x - ( - 3 ) ) * ( x - 2 ) * ( x - 6 ) =
( x + 6 ) * ( x + 3 ) * ( x - 2 ) * ( x - 6 ) =
x ^ 4 + x ^ 3 - 42 x ^ 2 -36 x + 216
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