Find all values of b or c that will make the polynomial a perfect square trinomial. 100r^2-60r+c

Key Concepts

Perfect Square Trinomial

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial. It takes the form (a ± b)² = a² ± 2ab + b². For a trinomial to be a perfect square, the first term must be a perfect square, the last term must also be a perfect square, and the middle term must be twice the product of the square roots of the first and last terms.

Identifying Coefficients

In the polynomial 100r² - 60r + c, the coefficients are the numerical factors of each term. Here, 100 is the coefficient of r², -60 is the coefficient of r, and c is the constant term. Understanding how to identify and manipulate these coefficients is crucial for determining the conditions under which the polynomial becomes a perfect square trinomial.

Condition for Perfect Square

To determine the value of c that makes the polynomial a perfect square trinomial, we need to ensure that the middle term (-60r) equals twice the product of the square roots of the first term (10r) and the last term (√c). This leads to the equation -60 = 2 * 10 * √c, which can be solved to find the appropriate value of c.