Question

If one of the zeroes of the polynomial g(x) = (k² + 4)x² + 13x + 4k is the reciprocal of the other then k =
a) 2
b)-2
c) 1
d)-1

Answer 1

✴️ Your answer is a) 2

Explanation ❇️

Answer:

Answer:The value of k is 2.

Answer:The value of k is 2.Step-by-step explanation:

Answer:

The value of k is 2.

Step-by-step explanation:

Given : If one zero of the polynomial f(x) = (k^2+4)x^2+13x +4kf(x)=(k2 +4)x2+13x+4k is reciprocal of he other.

To find : The value of k ?

Solution :

Let the one zero of the polynomial be$\alphaα$

Then the other zero of the polynomial be$\frac{1}{\alpha} </p><p>α</p><p>1</p><p> </p><p>$

f(x) = (k^2+4)x^2+13x +4kf(x)=(k

2

+4)x

2

+13x+4k

Here, a=k^2+4a=k

2

+4 , b=13 and c=4k

The product of zeros of quadratic function is

$\alpha \times \frac{1}{\alpha }=\frac{c}{a}α× </p><p>α</p><p>1</p><p> </p><p> = </p><p>a$

c

$</p><p>1=\frac{4k}{k^2+4}1= </p><p>k </p><p>2</p><p> +4</p><p>4k</p><p> </p><p>$

k^2+4=4kk

2

+4=4k

k^2-4k+4=0k

2

−4k+4=0

k^2-2k-2k+4=0k

2

−2k−2k+4=0

k(k-2)-2(k-2)=0k(k−2)−2(k−2)=0

(k-2)(k-2)=0(k−2)(k−2)=0

i.e. k-2=0k−2=0

k=2k=2

Therefore, The value of k is 2.

Answer 2

Hey mate ,

Let the zeros be x and 1/x

Thus product of zeros = c/a

x × 1/x = k^2+4 / 4k

1 = 4+k^2 /4k

k^2 +4 = 4k

k^2 - 4k +4 = 0

k^2 - 2k - 2k + 4 = 0

k(k-2) -2 (k-2) = 0

(k-2)(k-2) = 0

k = +2

option (a)

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