Let p(x) be a quadratic polynomial such that p(1) = p(-1) = 0 . What is the coefficient of x in p(x) ?

Step-by-step solution

Let p(x) = ax^2 + bx + c be the quadratic polynomial, where a 0 . Given p(1) = 0 , we have a + b + c = 0 . Given p(-1) = 0 , we have a - b + c = 0 . Subtracting the second equation from the first gives 2b = 0 , which implies b = 0 . Alternatively, since the roots of the quadratic polynomial are 1 and -1 , the sum of the roots is 1 + (-1) = 0 . Using the relation between roots and coefficients, the sum of the roots is - b a = 0 , which gives b = 0 . Therefore, the coefficient of x in p(x) is 0 . Answer: 0