Question

If the zeroes of the polynomial 3x^2 - 11x + k are reciprocal to each other, then the value of k is:

a) 3

b) 11

c) 1

d) 33

Answer 1

To find the value of k in the polynomial 3x² - 11x + k, if the zeroes are reciprocal to each other, we can solve for the zeroes by setting them as a and 1/a. The sum of the zeroes is a + 1/a = 11/3, and the product of the zeroes is a * (1/a) = 1. Using these equations, we can solve for a and find that k = a * (1/a) = -1/3 * 3 = -1. So, the value of k is c) 1.

Step-by-step explanation:

To find the value of k in the polynomial 3x² - 11x + k, if the zeroes are reciprocal to each other, we can use the fact that if a and b are reciprocals of each other, then a * b = 1.

In this case, the zeroes are reciprocal to each other, so let the zeroes be a and 1/a. The sum of the zeroes is a + 1/a = 11/3, and the product of the zeroes is a * (1/a) = 1.

Using these equations, we can solve for a:

a + 1/a = 11/3

a² + 1 = 11/3 * a

3a² + 3 = 11a

3a² - 11a + 3 = 0

Using the quadratic formula, we find that a = -1/3 and 3. Therefore, the value of k is the product of the zeroes, which is k = a * (1/a) = -1/3 * 3 = -1.

So, the correct answer is c) 1.