Factorisation Of Polynomials

The given cubic polynomial is .
The roots (zeroes) of this polynomial are denoted by .
According to Viète's formulas, for a cubic polynomial , the relations between the coefficients and the roots are:

Here, , , , and .
We need to find the value of :

Hence, the value of is .

We are given that is a factor of the polynomial:

Step 1: Factor Theorem

Since is a factor, substituting into must yield 0:

Step 2: Solving for

Final Answer: .

We are given that the sum and product of the zeroes of a quadratic polynomial are:

,

.

Step 1: General Form of Quadratic Polynomial

The quadratic polynomial whose roots are and is given by:

Step 2: Substituting Given Values

Final Answer: .