Question

Find a quadratic polynomial with zeroes -2 and -1/3​

Answer 1

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Step-by-step explanation:

Let the zeroes be α and β  

Then α + β = - 5 and  αβ = 6

The quadratic polynomial whose sum and product of the zeroes are given is given by :

x² - (α+β)x + αβ  

⇒ Then the quadratic polynomial will be :

⇒ x² - (-5)x + 6  

⇒ x² + 5x + 6  

This is your answer.

Hope this Helps !

Answer 2

Answer:

3x²+7x+2

Step-by-step explanation:

α=(-2), β=(-1/3)

Quadratic polynomial

=x²-(α+β)x+αβ

=x²-[(-2)+(-1/3)]x+(-2)×(-1/3)

=x²-(-2-1/3)x+2/3

=x²-(-6-1)/3x+2/3

=x²+7/3x+2/3

Multiply each term by 3

=x²×3+7/3x×3+2/3×3

=3x²+7x+2