Question

Find a cubic polynomial whose zeroes are 5,3,and-2

Answer 1

Answer:

or given roots are 3,5,−2

therefore the cubic equation with above roots are (x−3)(x−5)(x−2)

simplifying it we get

(x−3)(x−5)(x+2)=(x2−8x+15)(x+2)=x3−6x2−x+30

Answer 2

Concept

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 of which are real numbers. An equation involving a cubic polynomial is called a cubic equation

For a polynomial, there may be some values of the variable for which the polynomial will be zero. These values are called the zeros of the polynomial.

Given

It is given that Zeros of a polynomial are 5,3,and-2

Find

We need to find a cubic polynomial

Solution

Let x=5 , x =3 ,x=-2 be the zeros of the polynomial

Then the cubic polynomial is given by

(x - 5) (x - 3) (x + 2)

=(x^2 - 3x - 5x + 15) (x + 2)

=(x^2 - 8x + 15) (x+2)

=x^3 + 2x^2 -8x^2 -16x +15x +30

=x^3 - 6 x^2 - x + 30

Hence the cubic polynomial is x^3 - 6 x^2 - x + 30

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