Question

find the quadratic polynomial whose zeros are in ratio 2x:3x and the sum is 15

Answer 1

let the zeros be 2x and 3x

2x + 3x = 15

5x = 15

x = 3 thus two zeros are 2*3 = 6 and 3*3 = 9

product of zeros = 6*9 = 54
.
thus equation will be k( x2 - (sum of zeros)x + product of zeros) where k is real

k(x2 - 15x +54)

k =1 eq = x2-15x +54

hope it helped

Answer 2

Ratio of zeros is 2x:3x
Sum of zeros=15
2x+3x=15
5x=15
x=3
Using in ratios
2x=6
3x=9
Sum of zeros=9+6=15 (given)
Product of zeros=9×5=54
For quadratic polynomial
Plz check the picture