Question

B. Find a polynomial equation with integer coefficients that has the following

roots.

1. 1, -2, -5

2 +1, 2

3. +2, +3

4. -1, 2, -1/2

5. 2/5, -1/3, +3​

Answer 1

Answer:

1) express the root as set of factors

x=1 , x= -2 , x= -5

so x-1=0 , x+2=0 , x+5=0

multiply the 3 set of factors

(x-1)(x+2)(x+5)=0

(x^2+x-2)(x+5)=0

so (x^3+6x^2+3x-10)=0

2)express the root as set of factors

x=1 , x=2

so x-1=0 , x-2=0

multiply the 2 set of factors

(x-1)(x-2)=0

so (x^2-3x+2)=0

3)express the root as set of factors

x=2 , x=3

so x-2=0 , x-3=0

multiply the 2 set of factors

(x-2)(x-3)=0

so (x^2-5x+6)=0

4)express the root as set of factors

x= -1 , x=2 , x= -1/2

so x+1=0 , x-2=0 , x+(1/2)=0=2x+1

multiply the 3 set of factors

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

=>(x^2-x-2)(2x+1)=0

=>(2x^3-x^2-5x-2)=0

5)express the root as set of factors

x=2/5 , x= -1/3 , x=3

so x-(2/5)=0=5x-2 , x+(1/3)=0=3x+1 , x-3=0

multiply the 3 set of factors

(5x-2)(3x+1)(x-3)=0

=>(5x-2)(3x^2-8x-3)=0

=>(15x^3-40x^2-15x-6x^2+16x+6)=0

=>(15x^3-46x^2+x+6)=0