Question

Find a polynomial / (1) of degree 4 that has the following zeros.
0, 5, 6, 1

Answer 1

`\bf \begin{cases} x = 0&x = 0\\ x = 5\implies &x-5=0\\ x= 6\implies &x-6=0\\ x=1\implies &x-1=0 \end{cases}\qquad \qquad \qquad (x)(x-5)(x-6)(x-1)=\stackrel{y}{0} \\\\\\ (x)\stackrel{F~O~I~L}{(x^2-11x+30)}(x-1)=y\implies (x^3-11x^2+30x)(x-1)=y \\\\\\ x^4-11x^3+30x^2-x^3+11x^2-30x=y\implies x^4-12x^3+41x^2-30x=y`