Question

Find a quadratic polynomial whose zeros are in the ratio 2 is to 3 and their sum is 15

Answer 1

Let the 2 nos. be 2x and 3x.
2x+3x=15
=>5x=15.
=>x=3.
Hence,the 2 nos.are 6 and 9.
a + b = 6+9 = 15
ab = 6×9=54.
Polynomial ->x²+(a+b)x+ab
->x²+15x+54.

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Answer 2

Let the zeros be 2x and 3x

2x + 3x = 15

5x=15
x=15/5

x=3

Thus two zeros are 2*3=6
                                 3*3=9