Question

given that the 0's of the cubic polynomial f ( x )= xcube - 6xsquare + 3 x + 10 are of the form a,a+b,a+2b for some real numbers a and b ,find the values of a and b as well as the zeroes of given polynomial

Answer 1

=-1, b=3 is the solution.{ a, a+b, a+2b are in A.P. therefore the zeros can be a-d, a, a+d.We have sum of zeros = -b/a i.e, a-d, a, a+d=-(-6)/1. and solving this we get a=2.Now, product of zeros =c/a i.e, (a-d)* a*(a+d)=3/1. Putting a=2 in this equation we get d=3. Hence we obtain the zeros of polynomial as a-d=-1, a=2, a+d=5. therefore the zeros of given polynomial are -1, 2, and 5. Now clearly these are in A.P. with first term a= -1, and common difference=b=3 which is of the form a, a+b, a+2b. Hence a=-1, and b=3 is the solution . for verification , use the relation of a cubic polynomial with its zeros.} Thank you........