An algebra problem by Anandmay Patel
A quadratic polynomial is such that the sum of the zeroes of the polynomial is equal to their product. If the polynomial is , then which of the following must be the value of ?
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1 solution
If a quadratic polynomial has x = p and q for its roots, then (x - p)(x - q) = 0 => x^ - (p+q) x + pq = 0 where p+q = pq. Taking the quadratic equation a x^2 + bx + c = 0 => x^2 + (b/a)*x + c/a 0, just set b/a = -(p+q) and c/a = pq which implies -b/a = c/a, or b = -c.