Question

Find the roots of the polynomial

Answer 1

Answer:

Please do type the question.

But the general formula to find the roots of a polynomial is:

-$\sqrt{b^{2} -4ac}\\------------------------\\ 2a$

Answer 2

Answer:

Roots of Polynomials Formula

The polynomials are the expression written in the form of:

anxn+an-1xn-1+……+a1x+a0

The formula for the root of linear polynomial such as ax + b is

x = -b/a

The general form of a quadratic polynomial is ax2 + bx + c and if we equate this expression to zero, we get a quadratic equation, i.e. ax2 + bx + c = 0.

The roots of quadratic equation, whose degree is two, such as ax2 + bx + c = 0 are evaluated using the formula;

x = [-b ± √(b2 – 4ac)]/2a

The formulas for higher degree polynomials are a bit complicated.

Roots of three-degree polynomial

To find the roots of the three-degree polynomial we need to factorise the given polynomial equation first so that we get a linear and quadratic equation. Then, we can easily determine the zeros of the three-degree polynomial. Let us understand with the help of an example.

Example: 2x3 − x2 − 7x + 2

Divide the given polynomial by x – 2 since it is one of the factors.

2x3 − x2 − 7x + 2 = (x – 2) (2x2 + 3x – 1)

Now we can get the roots of the above polynomial since we have got one linear equation and one quadratic equation for which we know the formula.

Also, read:

Polynomial Division

Polynomial For Class 10

Polynomials Class 9

Finding Roots of Polynomials

Let us take an example of the polynomial p(x) of degree 1 as given below:

p(x) = 5x + 1

According to the definition of roots of polynomials, ‘a’ is the root of a polynomial p(x), if

P(a) = 0.

Thus, in order to determine the roots of polynomial p(x), we have to find the value of x for which p(x) = 0. Now,

5x + 1 = 0

x = -1/5

Hence, ‘-1/5’ is the root of the polynomial.