Question

What is the product of the roots of x^2-4x+k=0 if one of the roots is 7?

Please show the steps:)

Answer 1

http://www.mathsisfun.com/algebra/polynomials-remainder-factor.html <--- recall the remainder theorem?

Answer 2

If x=7 is a root, then \[(7)^2-4(7)+k=0\]From that, you can find the value of \(k\). Once you know the entire equation, you can find the other root in a number of ways. One is to just factor it (should be easy, you already know one of the factors), or divide out (x-7), or use the quadratic formula, or recall that the constant term is always the product of the constant terms of the factor binomials, which means that -7 * -<other root> = k, etc.