Question

If the sum of zeroes of the quadratic polynomial 2x^2-(2k+1) x+(3k-1) is half of the product of its zeroes. Find value of k?

Answer 1

K = -1/7

Given :

Quadratic polynomial 2x^2 - (2k+1)x + (3k-1)

The sum of the zeroes of the above polynomial is equal to half of the product of its zeroes

To find :

Value of "k"

Explanation :

Let the zeroes be "x" and "y" , Then according to the quesion :

➡ x + y = 1/2 × xy

Sum of the zeroes = x+y = -b / a = -2k-1/2

b = -(2k+1) = - 2k-1

a = 2

Product of the zeroes = xy = c / a = 3k-1/2

c = 3k-1

a = 2

Putting the values :

➡ -2k -1/2 = 1/2 × 3k-1/2

➡ -2k-1/2 = 3k-1/4

➡ -2k-1 = 3k-1/2

➡ -4k-2 = 3k-1

➡ -4k-3k = -1+2

➡ -7k = 1

➡k = -1/7