Question

write
the relation between zeroes and
Co-effocients​

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

Polynomials can be linear (x), quadratic (x2), cubic (x3) and so on, depending on the highest power of the variable.

The number of zeroes of a polynomial is equal to the degree of the polynomial, and there is a well-defined mathematical relationship between the zeroes and the coefficients. Mathematically, if p(x) is a polynomial in x, and if k is any real number, then the value obtained by replacing x by k in p(x) is called the value of p(x) at x = k and is denoted by p(k).

Here, the real number k is said to be a zero of the polynomial of p(x), if p(k) = 0.

Simply put, the zeroes of a polynomial function are the solutions to the equation you get, when you set the polynomial equal to zero.

Let us understand the difference between zeros and roots in a polynomial equation.

A zero is a value for which a polynomial is equal to zero.

When you set a polynomial equal to zero, then you have a polynomial equation where the equations roots are same as the polynomial’s zeroes.

A root is a value for which a polynomial equation is true.

Example: The polynomial x-5 has one zero, that is x = 5. And the polynomial equation x-5 = 0 has one root, that is, x = 5.

The number of zeroes of a polynomial is equal to the degree of the polynomial, and there is a well-defined mathematical relationship between the zeroes and the coefficients.

Linear Polynomial

Any equation of the first degree is known as a linear equation. It is an equation of the form ax+b = 0, where and b are constants and x is a variable.

The general form of a linear polynomial is p(x) = ax+b, its zero is −ba = −(constantterm)(coefficientofx)

Quadratic Polynomial

General form of a quadratic polynomial is ax2 + bx + c where a ≠ 0. There are two zeroes, say α and β of a quadratic polynomial, where

Sum of the roots = α+β= −ba = −(coefficientofx)(coefficientofx2)

Product of the toots = αβ= ca = (coefficientofx)(coefficientofx2)

Cubic Polynomial

If α,β,γ are the zeros of a cubic polynomial p(x) = ax3+bx2+cx+d, then

α+β+γ=−ba

αβ+βγ+γα=ca

αβγ=−da

Hope it helped you mate!!