Question

If one zero of a polynomial x^2−3x+2k is reciprocal of other, find k.

Answer 1

Let $\alpha$ be the first root of the polynomial x² - 3x + 2k

Now, According to Question, other root is

$\frac{1}{ \alpha }$

Now, Product of roots = $\frac{Constantterm}{Coefficient\:of\:x^2}$

$\alpha \times \frac{1}{ \alpha } = \frac{k}{1} \\ \\ k = 1$

So, k = 1

Answer 2

Answer:

Let \alphaα be the first root of the polynomial x² - 3x + 2k

Now, According to Question, other root is

\frac{1}{ \alpha }

α

1

Now, Product of roots = \frac{Constantterm}{Coefficient\:of\:x^2}

Coefficientofx

2

Constantterm

\begin{lgathered}\alpha \times \frac{1}{ \alpha } = \frac{k}{1} \\ \\ k = 1\end{lgathered}

α×

α

1

=

1

k

k=1

So, k = 1