Question

if alpha, and beta are the zeros of a polynomial such that alpha +beta=10 and alpha x beta =6 then write the polynomial ​

Answer 1

Answer:

x² - 10x + 6

Step-by-step explanation:

Given :

• α + β = 10
• αβ = 6

To Find : Quadratic Polynomial

Solution :

The required polynomial can be find by using :

→ p(x) = k [ x² - (α + β)x + αβ ]

• Putting known values in it.

→ p(x) = k [ x² - (10)x + 6 ]

→ p(x) = k [ x² - 10x + 6 ]

• Putting k = 1.

→ p(x) = x² - 10x + 6

Answer 2

Answer:

Step-by-step explanation:

Given :-

α + β = 10

αβ = 6

To Find :-

Quadratic Polynomial.

Formula or Identity to be used :-

Polynomial of x = x² - (α + β)x + αβ

Solution :-

Putting all values, we get

⇒ p(x) = x² - (α + β)x + αβ

⇒ p(x) = x² - (10)x + 6

⇒ p(x) = x² - 10x + 6

⇒  p(x) = x² - 10x + 6

Hence, the required polynomial is x² - 10x + 6.

Important Formulas :-

• There are three main methods for solving quadratic equations: Factorization Completing the square method Quadratic Equation Formula

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