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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