Question

lf the zeroes of the polynomial x2-px+q be in the ratio 2:3 prove that 6p2=25q

Answer 1

Two zeros are alfa & bita,Alfa/bita =2/3,alfa =2k & bita = 3k,alfa+bita = -b/a so, p = 5k  & alfa.bita = c/a so, q = 6k^2,Hence, 6*5*5*k^2 = 25*6*k^2,So LHS = RHS

Answer 2

Hello mate,

Here is your answer,

Let the zeroes be 2a and 3a.

Sum of 0's

p = 5a

a = p/5

Product of 0's

q = 6a2

q = 6(p/5)2

q = 6p2/25

6p2=25q