Question

The zeros of polynomial x²-5x+k are the reciprocal of each other then find the value of k

Answer 1

Hey!!!!

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We have

=> x² + 5x + k = 0

Given, zeros are reciprocal of each other

then let the zeros be alpha and beta

$then \: \alpha = \frac{1}{ \beta }$

(reciprocal)

We know


=>
$\alpha \beta = \frac{c}{a}$

Thus

=>
$\frac{1}{ \beta } \times \beta = k$

Cancelling beta

=> k = 1

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Hope this helps ✌️

Good Morning ;)

Answer 2

Hey

Here is your answer,

x^2-5x+k=0

Sum of zeroes = -b/a
Alpha+beta = 5

Product of zeroes =c/a
Alphaxbeta = k

Given:
The zeroes are the reciprocal of each other
Therefore,
5x1/5=k
k=1

Hope it helps you!