Question 18

If the roots of the equation $$x^{2}-px+54=0$$ are in the ratio 2 : 3 , then value of p is:

Solution

Let the roots of the equation be 2k and 3k.

Product of roots $$=2k\times3k$$

$$6k^2=54$$

$$k=\pm3$$

Sum of roots $$=2k+3k$$

$$5k=p$$

$$p=5\times \pm3$$

$$p=\pm15$$

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