(a) State the relation connecting the sum and the product of the zeros of a quadratic polynomial ax2+bx+c(a=0).
(b) If α and β are the zeros of a quadratic polynomial, write an expression for a general quadratic polynomial having α and β as its zeros and justify your answer.
(c) Explain, without using any numerical calculation, why multiplying this polynomial by a non-zero constant changes the shape of its graph but does not alter its zeros.