Free Polynomial Root Calculator determines the roots of a polynomial in a fraction of seconds. Just enter the polynomial expression details in the below-mentioned input field of the calculator and tap on the calculate button. The polynomial roots with explanation will appear on the screen as output.
Use '^' for exponent
What is meant by Polynomial Root?
Roots are the solutions of the polynomial equation and these are the values of the unknown variable. The equation with a degree of 2 is called a quadratic equation and it is in the form of ax² + bx + c = 0. In the above equation, a, b, c are the coefficients and x is the variable. The solution of variable x can be known by finding the roots of the quadratic equation. The formula of the quadratic equation roots is given as: x = [-b ± √(b² − 4ac)]/(2a) The formula to find the roots of the linear polynomial i.e ax + b is x = -b/a.
Steps to Calculate Polynomial Roots
The following are the steps to compute the polynomial root easily. Have a look at these simple steps and get the result.
1. Know the highest degree polynomial equation.
2. Apply either the quadratic equation formula or linear polynomial formula based on the degree of polynomial.
3. Substitute the values in the selected formula
4. Solve the problem and get the root value
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Polynomial Root with Example
Question: Find the roots of polynomial 14x² + 42x + 70..
The given polynomial is 14x² + 42x + 704
After factoring we get 14(x² + 3x + 5)
By expanding the summation:
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
So, x² + 3x + 5 = 0
The coefficients of above quadratic equation are a = 1, b = 3 and c = 5
The formula of quadratic equation root is x = [-b ± √(b² − 4ac)]/(2a)
x = [-3 ± √(3² − 4 * 1 * 5)]/(2 * 1)
= [-3 ± √(9 − 20)]/2
= [-3 ± √-11]/2
= [-3 + √11 i]/2 or [-3 - √11 i]/2
Therefore, the roots of polynomial 14x² + 42x + 70 are [-3 + √11 i]/2 or [-3 - √11 i]/2.
FAQs on Polynomial Root Calculator
1. How do you find the roots of a polynomial?
The steps to find the polynomial roots are given here. Make the equation P(x) = 0 by putting each factor value equal to 0 and solving for x.
2. How to get the discriminant?
The formula to find the discriminant of a 2nd order polynomial is Δ = b² − 4ac. So, use this formula and substitute the values to obtain the discriminant of the equation
3. What is meant by the polynomial equation?
In mathematics, a polynomial equation is defined as the algebraic equation that has variables, coefficients, constants, mathematical operators. A polynomial equation can have many terms with different exponents. The higher exponent value of the variable is called the degree of the equation.
4. Find the roots of the polynomial equation 15x² + 8x + 3?
Given polynomial equation is 15x² + 8x + 3 It is a quadratic equation in the form of ax² + bx + c. So, a = 15, b = 8, c = 3 The formula to find the roots of the quadratic equation is x = [-b ± √(b² − 4ac)]/(2a) x = [-8 ± √(8² − 4 * 15 * 3)]/(2 * 15) = [-8 ± √(64 − 180)]/(30) = [-8 ± √(-116)]/(30) = [-8 + √116i]/(30) and [-8 - √116i]/(30)