Question

if the sum of the reciprocals of the roots of the equation x^2-px +36 =0 is 5/12, then the value of p is​

Answer 1

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Answer 2

The value of p is 15.

Step-by-step explanation:

Given : If the sum of the reciprocals of the roots of the equation $x^2-px +36 =0$ is $\frac{5}{12}$

To find : The value of p ?

Solution :

Let $\alpha,\beta$ are the roots of the equation.

In equation $x^2-px +36 =0$

Here, a=1, b=-p and c=36.

The sum of roots $\alpha+\beta=-\frac{b}{a}$

$\alpha+\beta=-\frac{-p}{1}$

$\alpha+\beta=p$

The product of roots $\alpha\beta=\frac{c}{a}$

$\alpha\beta=\frac{36}{1}$

$\alpha\beta=36$

The sum of the reciprocals of the roots of the equation is

$\frac{1}{\alpha}+\frac{1}{\beta}=\frac{5}{12}$

$\frac{\alpha+\beta}{\alpha\beta}=\frac{5}{12}$

$\frac{p}{36}=\frac{5}{12}$

$p=\frac{5\times 36}{12}$

$p=15$

Therefore, the value of p is 15.

#Learn more

In the quadratic equation ax2 + bx + c = 0, if the sum of the roots is equal to the product of the roots, find the sum of the reciprocals of the roots.

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