# If sum of the Zeros of the Polynomial Ky^2+2y-3K is Twice their product of Zeros then Find the Value of K

By BYJU'S Exam Prep

Updated on: October 17th, 2023

If sum of the zeroe of the polynomial Ky^2+2y-3K is twice their product of zeros then find the value of K

To find the value of K for the given polyynomial, we will use the given steps:

• Use the formula for the sum of the zeros: sum of zeros = -coefficient of y / coefficient of y^2 and substitute the coefficients: sum of zeros = -2 / K.
• Use the formula for the product of the zeros: product of zeros = constant term / coefficient of y^2 and substitute the values: product of zeros = -3K / K = -3.
• Use the given information and simplify the equation to find the value of k.

## If sum of the Zeros of the Polynomial Ky^2+2y-3K is Twice their product of Zeros then Find the Value of K

Solution:

The given polynomial is Ky^2 + 2y – 3K.

The sum of the zeros of a quadratic polynomial is given by the formula: sum of zeros = -coefficient of y / coefficient of y^2.

In this case, the coefficient of y^2 is K, and the coefficient of y is 2. Therefore, the sum of the zeros is -2/K.

The product of the zeros of a quadratic polynomial is given by the formula: product of zeros = constant term / coefficient of y^2.

In this case, the constant term is -3K, and the coefficient of y^2 is K. Therefore, the product of the zeros is -3K / K = -3.

According to the information given, the sum of the zeros is twice their product. So we have:

-2/K = 2 * (-3) -2/K = -6

To solve for K, we can cross-multiply:

-2 = -6K

Dividing both sides of the equation by -6:

K = -2 / -6 K = 1/3

Therefore, the value of K is 1/3.