Question

1If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then find the polynomial.

Answer 1

Answer:

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Step-by-step explanation:

If S and P be the sum and product of zeroes of quadratic equation, then quadratic polynomial is given by

x² - Sx + P

Now, given S = α + β = -6 ... (1)

and P = αβ = 5...(2)

Putting (1) and (2) in the equation, we get

x² - (-6x) + 5

∴ The required polynomial is x² + 6x + 5

Answer 2

Step-by-step explanation:

Given :

Sum of zeroes (α + β) = -6

Product of zeroes (αβ) = 5

To find :

Polynomial p(x)

Solution :

We know,

Quadratic polynomial :

• x² - (Sum of zeroes)x + Product of zeroes

Substituting we get :

⇒ x² - (-6)x + (5)

⇒ x² + 6x + 5

∴ x² + 6x + 5 is the polynomial.

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