Question

if the roots of px2+qx+2 are reciprocal of each other then p= ​

Answer 1

hope it helps... thanks

Answer 2

If the zeroes of $px^{2}+qx+2$ are reciprocal of each other, then $p=2$.

Correct question:

If the zeroes of $px^{2}+qx+2$ are reciprocal of each other, then find $p$.

Concept to be used:

For a polynomial $p(x)=ax^{2}+bx+c$ with zeroes $\alpha$ and $\beta$, we have the following relations,

sum of the zeroes is $(-\dfrac{b}{a})$ and

product of the zeroes is $\dfrac{c}{a}$

Step-by-step explanation:

The given polynomial is $px^{2}+qx+2$

Let, $\alpha$ and $\dfrac{1}{\alpha}$ be the zeroes of the given polynomial.

Then by the relation between zeroes and coefficients, we have

$\alpha+\dfrac{1}{\alpha}=-\dfrac{p}{q}$ ... ... (1)

$\alpha\times\dfrac{1}{\alpha}=\dfrac{2}{p}$

$\Rightarrow 1=\dfrac{2}{p}$

$\Rightarrow \boxed{p=2}$

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