Answer :

medhavimahendra
let one zero be α then the other will be 1/α 
clearly from the above step we can see that the product of the roots is 1 so c/a=1
4k/k²+4=1

4k=k²+4
k²-4k+4=0
(k-2)(k-2)
hence k=2 

Answer:

The value of k is 2.

Step-by-step explanation:

Given : If one zero of the polynomial [tex]f(x) = (k^2+4)x^2+13x +4k[/tex] is reciprocal of he other.

To find : The value of k ?

Solution :

Let the one zero of the polynomial be [tex]\alpha[/tex]

Then the other zero of the polynomial be [tex]\frac{1}{\alpha}[/tex]

[tex]f(x) = (k^2+4)x^2+13x +4k[/tex]

Here, [tex]a=k^2+4[/tex], b=13 and c=4k

The product of zeros of quadratic function is

[tex]\alpha \times \frac{1}{\alpha }=\frac{c}{a}[/tex]

[tex]1=\frac{4k}{k^2+4}[/tex]

[tex]k^2+4=4k[/tex]

[tex]k^2-4k+4=0[/tex]

[tex]k^2-2k-2k+4=0[/tex]

[tex]k(k-2)-2(k-2)=0[/tex]

[tex](k-2)(k-2)=0[/tex]

i.e. [tex]k-2=0[/tex]

[tex]k=2[/tex]

Therefore, The value of k is 2.

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