Find roots (zeroes) of : F(x) = 2x3+7x2-33x-18

POLYNOMIAL Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is ONE of the above MENTIONED tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading COEFFICIENT

In this case, the Leading Coefficient is 2 and the Trailing Constant is -18.

The factor(s) are:

of the Leading Coefficient : 1,2

of the Trailing Constant : 1 ,2 ,3 ,6 ,9 ,18

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 20.00

-1 2 -0.50 0.00 2x+1

-2 1 -2.00 60.00

-3 1 -3.00 90.00

-3 2 -1.50 40.50

-6 1 -6.00 0.00 x+6

-9 1 -9.00 -612.00

-9 2 -4.50 90.00

-18 1 -18.00 -8820.00

1 1 1.00 -42.00

1 2 0.50 -32.50

2 1 2.00 -40.00

3 1 3.00 0.00 x-3

3 2 1.50 -45.00

6 1 6.00 468.00

9 1 9.00 1710.00

9 2 4.50 157.50

18 1 18.00 13320.00

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p NOTE that q and p originate from P/Q reduced to its lowest terms

In our case this means that

2x3+7x2-33x-18

can be divided by 3 different polynomials,including by x-3

hope it helps you ✌️✅✅✅