Find the quadratic polynomial whose sum and products of the zeros are 5 and -6​

Find the quadratic polynomial whose sum and products of the zeros are 5 and -6​

1 thought on “Find the quadratic polynomial whose sum and products of the zeros are 5 and -6​”

  1. Given :

    Given, the sum and product of zeroes of a polynomial are 5 and -6.

    To find :

    We have to find the polynomial with sum and product of its zeroes as 5 and -6 respectively.

    Solution :

    According to the question :

    • Product of zeroes = αβ = -6
    • Sum of zeroes = α+β = 5

    We know that :

    • Polynomial = x² – (Sum of zeroes)x + (Product of zeroes)

    Substituting the given values :

    • Polynomial = x² – (5)x + (-6)
    • Polynomial = x² – 5x – 6

    Therefore, the polynomial whose sum and product of zeroes are 5 and -6 respectively is x² – 5x – 6.

    Know more :

    • Product of zeroes (αβ) = c/a
    • Sum of zeroes (α+β) = -b/a
    • Product of zeroes (αβγ) = -d/a
    • Sum of zeroes (α+β+γ) = -b/a
    • Sum of zeroes (αβ+βγ+γα) = c/a

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