Question

Write the polynomial, the product and sum of whose zeroes are -9 upon 2 and -3 upon 2 respectively.

Answer 1

Given

$\sf\longrightarrow{Sum\: of\: zeroes = \dfrac{-3}{2}}$

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$\sf\longrightarrow{Product\: of\: zeroes = \dfrac{-9}{2}}$

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To find

• The required polynomial.

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★ Let the zeroes of the polynomial be α and β.

$\rm\longmapsto{\alpha + \beta = \dfrac{- coefficient\: of\: x}{coefficient\: of\: x^2}}$

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$\rm\longmapsto{\alpha + \beta = \dfrac{-b}{a} = \dfrac{-3}{2}}$

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★ Similarly

$\rm\longmapsto{\alpha \beta = \dfrac{Constant}{Coefficient\: of\: x^2}}$

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$\rm\longmapsto{\alpha \beta = \dfrac{c}{a} = \dfrac{-9}{2}}$

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★ We know that

$\: \: \: \: \: \: \: \: \: \: \boxed{\bf{\orange{Polynomial = ax^2 + bx + c}}}$

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Here,

• a = 2
• b = 3
• c = -9

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★ Putting the values

$\tt:\implies\: \: \: \: \: \: \: \: {Polynomial = (2)x^2 + (3)x + (-9)}$

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$\bf:\implies\: \: \: \: \: \: \: \: {Polynomial = 2x^2 + 3x - 9}$

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Hence,

• Required Polynomial = 2x² + 3x - 9.

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Answer 2

Answer:

2x^2+3x-9

Step-by-step explanation:

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