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 BYJU'S Exam Prep
Updated on: October 17th, 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
Table of content
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.
Answer
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.
Similar Questions:
- Find the Zeros of the Quadratic Polynomial 4u²+8u and Verify the Relationship between the Zeros and the Coefficient.
- Write the Zeros of the Quadratic Polynomial f(x) = 4√3x² + 5x – 2√3
- For the Following, Find a Quadratic Polynomial whose Sum and Product Respectively of the Zeros are as Given. Also Find the Zeroes of the Polynomial by Factorization: 21/8, 5/16
- Find the Zeros of the Quadratic Polynomial √3x² – 8x + 4√3
- If α and β are the Zeros of the Quadratic Polynomial f(x) = ax2 + bx + c, then Evaluate
