# Find the Roots/Zeros Using the Rational Roots Test f(x)=4x^2-25

If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.
Find every combination of . These are the possible roots of the polynomial function.
Substitute the possible roots one by one into the polynomial to find the actual roots. Simplify to check if the value is , which means it is a root.
Simplify the expression. In this case, the expression is equal to so is a root of the polynomial.
Simplify each term.
Apply the product rule to .
Raise to the power of .
Raise to the power of .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Subtract from .
Since is a known root, divide the polynomial by to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
Next, find the roots of the remaining polynomial. The order of the polynomial has been reduced by .
Place the numbers representing the divisor and the dividend into a division-like configuration.
The first number in the dividend is put into the first position of the result area (below the horizontal line).
Multiply the newest entry in the result by the divisor and place the result of under the next term in the dividend .
Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.
Multiply the newest entry in the result by the divisor and place the result of under the next term in the dividend .
Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.
All numbers except the last become the coefficients of the quotient polynomial. The last value in the result line is the remainder.
Simplify the quotient polynomial.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite as .
Simplify the numerator.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Simplify the denominator.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Find the Roots/Zeros Using the Rational Roots Test f(x)=4x^2-25