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  • If the root of x² + px + 12 = 0 are in the ratio 1:3 then what is the value of p ?

If the root of x² + px + 12 = 0 are in the ratio 1:3 then what is the value of p ?

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Let the roots of the given equation  = $$alpha, 3alpha$$

Now, According to the given equation

                                                       $$alpha + 3 alpha = - p $$\$$ and $$ alpha imes 3 alpha = 12$$\$$ $$Rightarrow 4alpha = -p$$\$$ $$ alpha^2 = 4$$\$$ $$ alpha = +2, -2 $$\$$

put the value,

                           $$ 4(2) = -p and 4(-2) = -p $$\$$ $$ Rightarrow p = -8, +8 $$

Posted by

Deependra Verma

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