Question

a and 1/a are the two zeroes of the polynomial p(y) = 4 - k-y + 2y. Find the value of k.

Answer should be -2​

Answer 1

Answer:

The value of the k is 4.

Step-by-step explanation:

For this question, we have to put the zeroes which are given above in the equation and then calculate the value of k. The zeroes of the polynomial are given as follows: a and 1/a

p(y) = 4 - k-y + 2y.

Therefore putting y = a

p(a) = 4 - k-a + 2a = 0

⇒ 4 - k + a = 0

⇒ - k + a = - 4 equation 1

Now we are put y = 1/a

∴ p(1/a) = 4 - k - 1/a + 2 × 1/a = 0

⇒ 4 - k -1/a + 2/a = 0

⇒ 4 - k + 1/a = 0

⇒ - k + 1/a = -4 equation 2

Since we have the two equations are equal we can write,

∴ - k + 1/a =  - k + a

⇒ - k + k + 1/a - a = 0

⇒ 1/a - a = 0

⇒ 1/a = a

⇒ 1 = $a^{2}$

⇒ a = 1

Now putting the value a = 1 in first equation we have,

- k + a = -4

⇒ - k + 1 = -4

⇒ - k = -4 -1

⇒ k = 5

Therefore we have the value of k = 5.