FIND THE ANSWER FOR 5 AND
6
Exercise 10.4. Consider a quadratic polynomial x2 + bx + c, with b and c real and with nonnegative discriminant, so that the roots ri and r2 are real.
1.Recall that c= r1r2 and b = -(r1 +r2) 2. If c = 0, then the nature of the roots is easy to determine. Explain why 3. Assume that c 0. Show that if the roots r1 and r2 have the same sign. then c > 0, and if the roots have opposite sign, then c < 0. 4. Conclude that there is an odd number of positive roots when c is negative and an even number when c is positive. 5. Assume that c is positive. Show that the two roots are both positive precisely when b < 0 and both negative precisely when b > 0. 6. Conclude that you can use b and c to determine the signs of the roots. Describe exactly how you would do so.