Question

If two zeroes of the polynomial x - 4x -3x +16x -4 are 2+√3 and 2-√3​

Answer 1

Sol. (i) x2 – 2x – 8

We have p(x) = x2 – 2x – 8

= x2 + 2x – 4x – 8 = x (x + 2) – 4 (x + 2)

= (x – 4) (x + 2)

For p(x) = 0, we have

(x – 4) (x + 2) = 0

Either x – 4 = 0 ⇒ x = 4

or x + 2 = 0 ⇒ x = – 2

∴ The zeroes of x2 2x – 8 are 4 and –2.

Now, sum of the zeroes

Thus, relationship between zeroes and the coefficients in x2 – 2x – 8 is verified.

(ii) 4s2 – 4s + 1

We have p(s) = 4s2 – 4s + 1

= 4s2 – 2s – 2s + 1 = 2S (2S – 1) –1 (2s – 1)

= (2s – 1) (2s – 1)

For p(s) = 0, we have,