Question

If zeries the polynomial. X²-px+q are in the ratio 2:3 prove that6p² =25q

Answer 1

a=1 , b=(-p) , c=q

Let, it be 2k and 3k

Sum of zeroes:

2k +3k=-b/a

5k=-(p)

5k=p

25k²=p² [squaring both sides]

k²=p²/25 .......(1)

Product of the zeroes:

2k*3k=c/a

6k²=q

k²=q/6.....(2)

Comparing (1) and (2)

p²/25=q/6

Ans- 25q=6p²