Question

If the sum of the squares of the zeroes of the polynomials 6x^2+x+k is 25/36. Find the value of 'k'

Answer 1

Hi ,

Let p( x ) = 6x² + x + k ,

Let m , n are two zeroes of p ( x ) ,

compare p ( x ) with ax² + bx + c , we get

a = 6 , b = 1 , c = k

sum of the zeroes = -b/a

m + n = - 1/6 ---( 1 )

mn = c/a

mn = k/6 ----( 2 )

sum of the squares of the zeroes = 25/36

m² + n² = 25/36----( 3 )

do the square of equation ( 1 ) , we get

( m + n )² = (- 1/6 )²

m² + n² + 2mn = 1/36

25/36 + 2 ( k/6 ) = 1/36

k/3 = 1/36 - 25/36

k/3 = ( 1 - 25)/36

k/3 = - 24/36

k = ( - 24 × 3 )/36

k = -2

I hope this helps you.

: )