Question
Asked Nov 22, 2019
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Write an equation of least degree with intergral coefficents that has the given zeros.

-4, 2, 5

Explanation please. 

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Expert Answer

Step 1

We know:

We can see that there are three zeros of the given functi on, i.e -4,2,5
Now, we also know that if x
is a factor of f(x)
a is a zero of the function f(x), then (x-a)
Thus, for least degree of equation, we need atleast three factors for each of the
three zeros
So, the least degree of the equation will be three.
Thus, x-(4))x-2).(x-5) will be the factors of f(x)
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We can see that there are three zeros of the given functi on, i.e -4,2,5 Now, we also know that if x is a factor of f(x) a is a zero of the function f(x), then (x-a) Thus, for least degree of equation, we need atleast three factors for each of the three zeros So, the least degree of the equation will be three. Thus, x-(4))x-2).(x-5) will be the factors of f(x)

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Step 2

If we multiply all the factors, ...

We can therefore write:
f ()x(4) x-2) (x-5)
f(x)(x+4)(x2-5x-2x+10)
f ()x+4)(x-7x +10)
_
f(x)x3 - 7x2 +10x +4x2 -28x + 40
=> f(x)x3-3x2-18x + 40
help_outline

Image Transcriptionclose

We can therefore write: f ()x(4) x-2) (x-5) f(x)(x+4)(x2-5x-2x+10) f ()x+4)(x-7x +10) _ f(x)x3 - 7x2 +10x +4x2 -28x + 40 => f(x)x3-3x2-18x + 40

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Math

Algebra

Polynomials