Question

For the cubic polynomial P (x)= x3-10x2+31x-30 the sum of the product of the zero taken two a time (-31,30,31)​

Answer 1

Answer:

Step-by-step explanation:

Given that,

Cubic polynomial p ( x ) = x³ - 10x² + 31x - 30

Comparing the given polynomial with ax³ + bx² + cx + d = 0 with zeroes α, β, γ.

We have a = 1 , b = - 10, c = 31 and d = - 30.

∴Sum of its zeroes = α + β + γ = - b / a = - ( - 10 ) / 1 = 10 and

Product of its zeroes = αβγ = - d / a = - ( - 30 ) / 1 = 30

∴The sum of the product of the zeroes taken two a time

= αβ + βγ + γα = c / a

= 31 / 1

= 31 is the answer.

Answer 2

Answer:

31 is the answer.

Step-by-step explanation:

A cubic polynomial is a type of polynomial based on the degree, i.e. the highest exponent of the variable. Thus, a cubic polynomial is a polynomial whose highest power of the variable or degree is 3. A polynomial is an algebraic expression with variables and constants with exponents as whole numbers.

A cubic polynomial is a polynomial with the highest exponent of the variable, i.e., the degree of the variable as 3. Based on the degree, the polynomial is divided into 4 types, namely zero polynomial, linear polynomial, quadratic polynomial, and cubic polynomial. The general form of a cubic polynomial is p(x): $ax^3 + bx^2 + cx + d$, a ≠ 0, where a, b, and c are coefficients and d is a constant, all real numbers. An equation involving a cubic polynomial is called a cubic equation.

Given that,

Cubic polynomial p ( x ) = $x^3 - 10x^2+ 31x - 30$

Comparing the given polynomial with ax³ + bx² + cx + d = 0 with zeroes α, β, γ.

We have a = 1 , b = - 10, c = 31 and d = - 30.

∴Sum of its zeroes = α + β + γ = - b / a = - ( - 10 ) / 1 = 10 and

Product of its zeroes = αβγ = - d / a = - ( - 30 ) / 1 = 30

∴The sum of the product of the zeroes taken two a time

= αβ + βγ + γα = c / a

= 31 / 1

= 31 is the answer.

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