Question

if the sum of zeros and the product of the zeros are √2 and -12 respectively ..find quadratic polynomial and zeros of the polynomial ...​

Answer 1

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Step-by-step explanation:

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Answer 2

Given -

• Sum of zeroes = √2
• Product of zeroes = -12

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To find -

1. Quadratic polynomial.
2. Zeroes of the polynomial.

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Solution -

Firstly, we have to find the quadratic polynomial.

We know that,

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★ p(x) = x² - (sum of zeroes)x + (product of zeroes)

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Therefore, the required quadratic polynomial will be

→ Polynomial = x² - (√2)x + (-12)

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→ Polynomial = x² - √2x - 12

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Hence,

• Required polynomial is x² - √2x - 12.

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Now, we have the polynomial and need to find zeroes of the polynomial.

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By middle term splitting

→ x² - √2x - 12 = 0

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→ x² - 3√2x + 2√2x – 12 = 0

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→ x(x - 3√2) + 2√2(x - 3√2) = 0

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→ (x - 3√2) (x + 2√2) = 0

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Finding zeroes

→ x - 3√2 = 0⠀⠀or⠀⠀x + 2√2 = 0

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→ x = 3√2⠀⠀⠀or⠀⠀x = -2√2

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Hence,

• Zeroes of the polynomial are 3√2 and -2√2.

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