If the product of the zeroes of the polynomial p(x) =2x2 minus 3x + k is 3 find the value of k
Hello,
The value of k is 6.
Explanation
1. Understand the Formula
For any quadratic polynomial in the standard form ax² + bx + c, the product of its zeroes (roots) is given by the formula:
Product of the zeroes = c/a
2. Identify the Coefficients
First, let's identify the values of a, b, and c from your given polynomial:
p(x) = 2x² - 3x + k
Comparing this to the standard form, we have:
• a = 2
• b = -3
• c = k
3. Set Up the Equation
The problem states that the product of the zeroes is 3.
Using the formula, we know the product of the zeroes is also c/a. So, we can set up the following equation:
c/a = 3
4. Solve for k
Now, substitute the values of 'a' and 'c' from the polynomial into the equation:
k/2 = 3
To find k, multiply both sides of the equation by 2:
k = 3 * 2
k = 6
Therefore, the value of k is 6.
