# If the sum of Zeros of the Quadratic Poynomial p(x) = kx²+2x+3k is Equal to their Product Find the Value of k.

By Mohit Uniyal|Updated : May 15th, 2023

If the sum of zeros of the quadratic poynomial p(x)=kx²+2x+3k is equal to their product find the value of k.

Here are the steps which can be used to solve the given problem and find the value of K quickly:

• Write down the quadratic polynomial and determine the sum and product of the zeros by using the formulas.
• Set up the equation using the sum and product of the zeros and then solve the equation by cross-multiplying

## Solution

We have the quadratic polynomial p(x) = kx² + 2x + 3k.

The sum of the zeros is -b/a, which in this case is -2/ k. The product of the zeros is c/a, which is 3k/k = 3.

According to the problem, the sum of the zeros is equal to their product. Therefore, we have:

-2/k = 3

To solve for k, we can cross-multiply and solve the resulting equation:

-2 = 3k

Dividing both sides by 3:

k = -2/3

Therefore, the value of k that satisfies the condition where the sum of the zeros is equal to their product in the given quadratic polynomial p(x) = kx² + 2x + 3k is k = -2/3.

If the sum of zeros of the quadratic poynomial p(x)=kx²+2x+3k is equal to their product, then the value of k = -2/3.

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