Question

Form a quadratic polynomials whose zeroes are 7+root 5 and 7-root 5

Answer 1

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• 7 + √5 = Zero of the polynomial

• 7 - √5 = Zero of the polynomial

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• Zeros of the polynomial is the value of the variable for which when replaced in the polynomial the value for the polynomial changes to zero.

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• x² - (α - β)x + αβ

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• Form a quadratic polynomials whose zeroes are 7 + √5 and 7 - √5

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   To Find α + β :

• α + β = 7 + √5 + 7 - √5

• α + β = 14

   To Find α·β :

• α·β = 7 + √5 × 7 - √5
• α·β = 7² - √5²        ∵ (a + b)(a - b) = a² - b²
• α·β = 49 - 5 = 44

   To Find Quadratic equation :

• x² - (α + β)x + αβ
• x² - (14)x + 44
• x² - 14x + 44