Question

find a quadratic polynomial the sum and product of whose zeroes are -3and2 respectively​

Answer 1

Given

• Sum of zeroes (α + ß) = -3
• Product of zeroes (αß) = 2

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To find

• The quadratic polynomial.

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Solution

• We have sum and product of the zeroes of a quadratic polynomial.

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{We\: know\: that}}}$

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$\large{\underline{\boxed{\bf{Polynomial = x^2 - (\alpha + \beta)x + (\alpha \beta)}}}}$

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\green{Required\: polynomial}}}$

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→ x² - (α + ß)x + (αß) = 0

→ x² - (-3)x + (2) = 0

→ x² + 3x + 2 = 0

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Hence,

• The required quadratic polynomial is

⠀⠀⠀⠀⠀❍ x² + 3x + 2 = 0

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