#1**+1 **

To find an equation that has the three solutions of 2, 4, and 5, first set each solution equal to x.

\(x=2\)

\(x=4\)

\(x=5\)

Next, figure out what number goes with each of the three solutions that makes x equal to zero on the right side. For x=2, the number will be -2; for x=4, the number is -4; for x=5, the number will be -5. What you do on the right side, you do to the left side as well.

\(x=2\)

\(x-2=2-2\)

**\(x-2=0\)**

\(x=4\)

\(x-4=4-4\)

**\(x-4=0\)**

\(x=5\)

\(x-5=5-5\)

**\(x-5=0\)**

Next, combine all three equations using the zero product.

\((x-2)\times(x-4)\times(x-5)=0\)

Next, expand the left side.

\((x-2)\times(x-4)\times(x-5)=0\)

\(({x}^{2}-4x-2x+8)\times(x-5)=0\)

\(({x}^{2}-6x+8)\times(x-5)=0\)

\({x}^{3}-5{x}^{2}-6{x}^{2}+30x+8x-40=0\)

\({x}^{3}-11{x}^{2}+38x-40=0\)

Next, replace 0 on the right side with y and then switch the equation around so that the y is on the left side.

\({x}^{3}-11{x}^{2}+38x-40=y\)

**\(y={x}^{3}-11{x}^{2}+38x-40\)**

gibsonj338
Aug 12, 2017

#1**+1 **

Best Answer

To find an equation that has the three solutions of 2, 4, and 5, first set each solution equal to x.

\(x=2\)

\(x=4\)

\(x=5\)

Next, figure out what number goes with each of the three solutions that makes x equal to zero on the right side. For x=2, the number will be -2; for x=4, the number is -4; for x=5, the number will be -5. What you do on the right side, you do to the left side as well.

\(x=2\)

\(x-2=2-2\)

**\(x-2=0\)**

\(x=4\)

\(x-4=4-4\)

**\(x-4=0\)**

\(x=5\)

\(x-5=5-5\)

**\(x-5=0\)**

Next, combine all three equations using the zero product.

\((x-2)\times(x-4)\times(x-5)=0\)

Next, expand the left side.

\((x-2)\times(x-4)\times(x-5)=0\)

\(({x}^{2}-4x-2x+8)\times(x-5)=0\)

\(({x}^{2}-6x+8)\times(x-5)=0\)

\({x}^{3}-5{x}^{2}-6{x}^{2}+30x+8x-40=0\)

\({x}^{3}-11{x}^{2}+38x-40=0\)

Next, replace 0 on the right side with y and then switch the equation around so that the y is on the left side.

\({x}^{3}-11{x}^{2}+38x-40=y\)

**\(y={x}^{3}-11{x}^{2}+38x-40\)**

gibsonj338
Aug 12, 2017