If zeros of p(x)=2x2-7x+k are reciprocals of each other,then find the value of me

If the roots are a and 1/a, then

a*1/a = k/2

k=2

2x^2-7x+2 has roots

(7±√33)/4
and, it happens that (7-√33)/4 = 4/(7+√33)

Let's first find the zeros of the quadratic equation p(x) = 2x^2 - 7x + k.

Let the zeros be a and 1/a (since the zeros are reciprocals of each other).

The sum of the zeros of a quadratic equation is given by the formula: a + (1/a) = (a^2 + 1)/a.

According to the given information, the sum of the zeros is -7/2. So we have:

(a^2 + 1)/a = -7/2.

Cross multiplying, we get:

2(a^2 + 1) = -7a.

Expanding, we have:

2a^2 + 2 = -7a.

Rearranging, we get:

2a^2 + 7a + 2 = 0.

To solve this quadratic equation for 'a', we can either factorize it or use the quadratic formula.

Let's use the quadratic formula: a = (-b ± √(b^2 - 4ac))/(2a), where a = 2, b = 7, and c = 2.

Substituting these values into the formula, we get:

a = (-7 ± √(7^2 - 4 * 2 * 2))/(2 * 2).

Simplifying:

a = (-7 ± √(49 - 16))/4.

a = (-7 ± √33)/4.

So, the zeros of the quadratic equation p(x) = 2x^2 - 7x + k are (7 + √33)/4 and (7 - √33)/4.

Since we need to find the value of 'me', and we don't know the value of 'k', we cannot determine the value of 'me' at this point.

To find the value of "k" when the zeros of the polynomial function p(x) = 2x^2 - 7x + k are reciprocals of each other, we can use the concept of the relationship between zeros and coefficients of polynomial functions.

Let's assume that the zeros of the function are "a" and its reciprocal "1/a". According to the given condition, we have:

a * (1/a) = 1 [Product of the zeros of a quadratic polynomial is 1]

Simplifying the above equation, we get:

1 = 1

This equation is always true, which means that any arbitrary value of "a" satisfies the condition. However, for the purpose of finding the value of "k," we can proceed with a specific value for "a."

Let's assume "a" = 2. Then its reciprocal is "1/a" = 1/2.

Now, substitute the values of "a" and "1/a" into the polynomial p(x):

p(x) = 2x^2 - 7x + k

p(x) = 2x^2 - 7x + k = 0 [Since "a" and "1/a" are the zeros]

Substituting a = 2, we get:

2 * 2^2 - 7 * 2 + k = 0

Simplifying the equation:

8 - 14 + k = 0

-6 + k = 0

k = 6

Therefore, the value of "k" is 6.

If zeroes of p(x) = 2x2

– 7x + k are reciprocal of each other, then find the value of k.