Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

# find a polynomial of degree 3 that's zeros 1,2 and -3 and in which the coefficient of x is -2?

thank you !!

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f(x) = -2 * (x - 1) * (x - 2) * (x - (-3))

f(x) = -2 * (x - 1) * (x - 2) * (x + 3)

f(x) = -2 * (x^2 - 3x + 2) * (x + 3)

f(x) = -2 * (x^3 + 3x^2 - 3x^2 - 9x + 2x + 6)

f(x) = -2 * (x^3 - 7x + 6)

f(x) = -2x^3 + 14x - 12

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• If 1 is a root, it means that you can factorize: (x - 1)

If 2 is a root, it means that you can factorize: (x - 2)

If - 3 is a root, it means that you can factorize: (x + 3)

It gives us:

= (x - 1).(x - 2).(x + 3)

= (x² - 2x - x + 2).(x + 3)

= (x² - 3x + 2).(x + 3)

= x³ + 3x² - 3x² - 9x + 2x + 6

= x³ - 7x + 6 → given that the coefficient of x is - 2 ? Perhaps the coefficient of x³ ?

= - 2.(x³ - 7x + 6)

= - 2x³ + 14x - 12

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• f(x) = a(x - 1)(x - 2)(x + 3)

f(x) = a( x³ - 7x + 6 )

f(x) = ax³ - 7ax + 6a

-7a = -2

∴ a = 2/7

f(x) = 2/7( x³ - 7x + 6 )

f(x) = 2/7x³ - 2x + 12/7

• JOHN
Lv 7
2 months agoReport

This is a good answer with a good method. I would have given you the BA.

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