Question

if alpha, beta are the zeroes of the polynomial, alpha+ beta = 10, alpha*beta=6. write the polynomials

Answer Fast

Answer 1

Answer :-

Given :-

• α + β = 10
• αβ = 6

To Find :-

• Quadratic Polynomial

Solution :-

Here, we are given sum of roots and product of roots.

We know that,

→ Sum of roots = -b/a

→ Product of roots = c/a

So,

→ -b/a = 10

→ c/a = 6

• a = 1
• b = -10
• c = 6

Substituting the value in general form of quadratic polynomial :-

Polynomial = x² - 10x + 6

Answer 2

A N S W E R :

• The required polynomial is p(x) = x² - 10x + 6.

Given :

• α + β = 10

• αβ = 6

To find :

• Find Quadratic Polynomial ?

Solution :

• The required polynomial can be find by using :

=> p(x) = k [x² - (α + β)x + αβ]

Substituting the values,

=> p(x) = k [x² - (10)x + 6]

=> p(x) = k [x² - 10x + 6]

=> Putting k = 1

=> p(x)² = x² - 10x + 6

Hence,

• The required polynomial is p(x) = x² - 10x + 6.