Find the polynomial function with roots 1, -2, and 5

Question

anonymous · Answer

Roots: 1,-2,5
Therefore, equation will be (x-1)(x+2)(x-5)=$$x^3 - 4x^2 - 7x + 10$$

mathmale · Answer

@sid0830:  Right.  But, could you possibly explain the principles you're using to work out this problem and guide the other person in finding his or her own answer?  Thanks.

anonymous · Answer

@mathmale  We know that if x=1, x=-2 and x=5 are the roots of a polynomial equation.
Hence, (x-1), (x+2) and (x-5) become the roots of the equation. ..........[Taking the constant to the LHS and making an equation eg. (x-1)=0, (x+2)=0 and (x-5)=0]

Once we have the factors of the equation, it is easy to find out the polynomial..is it clear now or do I need to give more explanation?