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Create an equation that has the three solutions x=2,4, and 5.

 
Guest Aug 12, 2017
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Best Answer 

 #1
avatar+1802 
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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
edited by gibsonj338  Aug 12, 2017
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1+0 Answers

 #1
avatar+1802 
+3
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
edited by gibsonj338  Aug 12, 2017

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