Question

How do you find the roots, real and imaginary, of `y=(2x-8)(x-2)-x^2+4x` using the quadratic formula?

Answer 1

The roots are `x=4" "or" "x=5/2`

Explanation:

`y=(2x-8)(x-2)-x^2+4x`
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`y=(2x-8)(x-2)-x(x-4)`
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`y=(2xxx-2xx4)(x-2)-(x-4)`
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`y=(2(x-4))(x-2)-(x-4)`
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`y=2(x-4)(x-2)-(x-4)`
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`y=(x-4)[2(x-2)-1]`
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`y=(x-4)[2x-4-1]`
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`y=(x-4)(2x-5)`
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We will find the roots when `y=0`
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`y=0`
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`rArr(x-4)(2x-5)=0`
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`x-4=0" "rArrx=4`
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`" "`OR
`2x-5=0rArr2x=5rArrx=5/2`
`" "`
The roots are `x=4" "or" "x=5/2`