Question

if the zeroes of the polynomial x square + kx + l are double of the zeroes of 2 x square - 5 x - 3 respectively then find the value of k and l​

Answer 1

We have k = - 5 and l = - 6

Step-by-step explanation:

The first polynomial is

f(x) = x² + kx + l

Let p, q are the zeros of f(x). Then

p + q = - k ..... (1)

pq = l ..... (2)

The second polynomial is

g(x) = 2x² - 5x - 3

= 2x² - 6x + x - 3

= 2x (x - 3) + 1 (x - 3)

= (x - 3) (2x + 1)

Then the zeros of g(x) are 3 and - 1/2.

Given that, p and q are double of 3 and - 1/2 respectively.

Let p = 2 × 3 = 6 and q = 2 × (- 1/2) = - 1

From (1), we get

6 - 1 = - k

or, 5 = - k

or, k = - 5

From (2), we get

6 (- 1) = l

or, - 6 = l

or, l = - 6

Therefore we have k = - 5 and l = - 6

Answer 2

After finding the values of g(x) when we are finding the value of people and q in bracket written:

Because zeroes of f(x) is doubled of zeroes of g(x)