(i) What is meant by the zeros of a quadratic polynomial?
(ii) For the quadratic polynomial 5x2−7x+2, find the sum and the product of its zeros.
(iii) The graph of y=5x2−7x+2 cuts the x–axis at two points. Using only the values obtained in part (ii), explain how the signs of the sum and product of the zeros help you to predict whether both intersection points lie to the right of the origin, to the left of the origin, or on opposite sides of the origin.
(iv) Verify your prediction by solving 5x2−7x+2=0 and stating the approximate positions of the zeros on the number line.