Question

Find the quadratic polynomial whose zeros are in the ratio 2:3 and their sum of 15.

Answer 1

Name them

Let the polynomial be a x² + b x + c

Let the roots be p and q

Given info :

p + q = 15

p : q = 2 : 3

Finding the roots

Let p be 2 k

Let q be 3 k

p + q = 15

==> 2 k + 3 k = 15

==> 5 k = 15

==> k = 15/5

==> k = 3

so : p = 2 k

          = 2 × 3

          = 6

q = 3 k

  = 3 × 3

  = 9

The polynomial

The polynomial has roots 6 and 9

So :

( x - 6 )( x - 9 ) = 0

==> x² - 6 x - 9 x + 54 = 0

==> x² - 15 x + 54 = 0

ANSWER :

x² - 15 x + 54 = 0

Hope it helps : )

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Answer 2

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