Question

find a cubic polynomial whoes zeroes are 4,-3,-1

Answer 1

This means that the polynomial must be :

( x - 4 )( x + 3 )( x + 1 ) = 0

[ only then the zeroes would be 4 , - 3 and - 1 ]

==> ( x - 4 )[ x ( x + 1 ) + 3 ( x + 1 ) ] = 0

==> ( x - 4 ) [ x² + x + 3 x + 3 ] = 0

==> ( x - 4 )( x² + 4 x + 3 ) = 0

==> x ( x² + 4 x + 3 ) - 4 ( x² + 4 x + 3 ) = 0

==> x³ + 4 x² + 3 x - 4 x² - 16 x - 12 = 0

Cancel 4 x² to get :

==> x³ - 13 x - 12 = 0

Yes this is the answer !!

The polynomial should be x³ - 13 x - 12 = 0

Hope it helps !

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Answer 2

so the roots of the equation is :-

x=1
x=-3 and
x= -1 respectively

we can write them as :-

x-1=0......(1)
x+3=0......(2)
x+1 =0......(3)

now multiply these 3 so that you will get a cubic polynomial

(x-1)(x+3)(x+1) = 0

( x²-1 ) (x+3) = 0

x³ + 3x² -x -3 = 0

hence dgree of polynomial is 3
so equation is cubic