Question 663893: write a polynomial of least degree for roots
1) 7,9,i,-i
2) 2,-2,6,-6
3) -2i,2i,3
4) 6,5,-3
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Since the roots are 7,9,-i,i
the factors, using x as the variable are;
(1) (x-7)(x-9)(x+i)(x-i), note the signs of factors are negative of the roots.
FOIL each pair, l-r, yields
(2) (x^2 -16x +63)(x^2+1) or
(3) x^4-16x^3+64x^2-16x+63
The second set is
(4) (x-2)(x+2)(x-6)(x+6) which simplifies to
(5) (x^2-4)(x^2-36) or
(6) x^4 -40x^2 + 144
The third set is
(7) (x+2i)(x-2i)(x-3) or
(8) (x^2+4)(x-3) or
(9) x^3 -3x^2 +4x -12
The last is
(10) (x-6)(x-5)(x+3). I'll let you FOIL this.
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