Question

if the two zeros of tge quadratic polynomial 7X2-15X-k are reciprocals of each other then find the value of K

Answer 1

Step-by-step explanation:

Given that: if the two zeros of the quadratic polynomial 7x²-15x-k are reciprocals of each other.

To find: Value of k

Solution:

Let

$\alpha\: and\: \beta$

are the zeroes of polynomial.

relation between coefficient of polynomial with its zeros are given by

$\alpha + \beta = \frac{ - b}{a}...eq1 \\ \\ \alpha \beta = \frac{c}{a}...eq2$

where a,b and C are coefficient of x²,x and constant term respectively.

here a=7,b=-15,c=-k

Here in the question given that, zeros are reciprocals to each other,thus if one zero is

$\alpha$

then other zero is

$\frac{1}{ \alpha }$

Now put the values in eq2

$\alpha \times \frac{1}{ \alpha } = \frac{ - k}{7} \\ \\ 1 = \frac{ - k}{7} \\ \\ \bold{k = - 7}$

Thus,

Value of k is -7.

Hope it helps you.

Answer 2

i hope this helps you

please Mark as brainlist