Question

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

Answer 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