Question

what is the zero of the polynomial 2x^3 + 6x^2 - 4x + 9

Answer 1

Step-by-step explanation:

$\bf \huge \: QUESTION \: \\\: \:$

• what is the zero of the polynomial $\tt 2x^3 + 6x^2 - 4x + 9$

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$\bf \huge \: GIVEN \: \\ \: \:$

• the polynomial $\tt</strong><strong> </strong><strong> </strong><strong>2x^3 + 6x^2 - 4x + 9</strong><strong>\:</strong><strong>\\</strong><strong> \:$

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$\bf \huge \: To \:Find \:\\ \:$

• what is the zero of the polynomial

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$\bf \huge \: \: Solving \\\: \:$

• A= 2
• B = 6
• C = -4
• D= 9

Let ,.

α,β and X be the √3

αβ = 3

Find the products of all the zeros:

$\tt αβ X = \frac{-d}{a} \:$

Then Putting the all values

$\tt αβ X= \frac{-9}{2} \:$

Find the third zeros:

We Have αβ = 3

$\tt 3X = \frac{-9}{2}\:$

$\tt X=\frac{-9}{2} ÷ 3 \:$

$\tt \red{ X= \frac{-3}{2} } \:$

The zero of polinomial is $\tt \red{ \frac{-3}{2} } \:</u></strong><strong><u> \\</u></strong><strong><u>$

Answer 2

Step-by-step explanation:

-3/2

Step-by-step explanation:

p(x) = 2x³ + 6x² – 4x + 9

Define α,β and γ

Let α,β and γ be the 3 roots

αβ = 3 (Given)

Find the products of all the zeros:

αβγ = - d/a

αβγ = - 9/2

Find the third zeros:

Given αβ = 3

3γ = -9/2

γ = -9/2 ÷ 3

γ = -3/2

Answer: The third zero is -3/2