Question

If one of the zeros of polynomial x^2 - 8 x + k is 7 times of other then find the value of k

Answer 1

Given Polynomial

f ( x ) = x² - 8x + k



$<b>Step I :</b>$ $<u>Assumption</u>$

A.T.Q.

Let the two zeroes be β and 7β.



$<b>Step II :</b>$ $<u>Determine a, b and c.</u>$

On comparing the given Polynomial with ax² + bx + c, we get

a = 1, b = - 8, c = k



$<b>Step III :</b>$ $<u>Determine the value of β by sum of zeroes.</u>$

Sum = β + 7β = 8β

Also, Sum = - b/a = - ( - 8 )/1 = 8

$\therefore$

8β = 8

β = 8/8 = 1



$<b>Step IV :</b>$ $<u>Determine the value of k by using product of zeroes.</u>$

Product = ( β ) ( 7β ) = 7β²

As we know, β = 1

So, Product = 7 ( 1 )² = 7

Also, Product = c/a = k/1 = k

$\therefore$

k = 7



$<u>Hence, the value of k is</u>$ $<b><u><I> 7.</u></b></I>$