Question

if the sum of zeroes of the polynomial x^2-(k+3)x+(5k-3) is equal to one fourth of the product of the zeroes find the value of k

Answer 1

Solution :

Let p(x) = x² - ( k + 3 )x + ( 5k-3)

Compare p(x) with ax² + bx + c , we

get

a = 1 , b = -( k + 3 ), c = 5k-3

i ) sum of the roots = -b/a

= - [-(k+3) ]/2

= ( k+3 )/2 ----( 1 )

ii ) Product of the roots = c/a

= ( 5k - 3 ) ----( 2 )

According to the problem given ,

( 1 ) = ( 1/4 ) of ( 2 )

=> ( k + 3 )/2 = ( 5k - 3 )/4

=> 4( k + 3 ) = 5k - 3

=> 4k + 12 = 5k - 3

=> 4k - 5k = -3 - 12

=> - k = -15

=> k = 15

Therefore ,

k = 15

•••••

Answer 2

Step-by-step explanation:

sum of zeros = 1/4product of the zeros

=. -b/a= 1/4 ( c/a)

= (k+3) = 1/4(5k-3)

= 4k+12= 5k-3

= k = 12+3

= k = 15