Question

find the zeroes of the quadratic polynomial x ^2-2x-3 and verify the relationship between the zeroes and the coefficient of the polynomial​

Answer 1

$\bf\underline{Solution:-}$

Given p(x) = x^2 - 2x - 3

On splitting the middle term, we have :

p(x) = x^2 - 2x - 3

p(x) = x^2 + 3x - x - 3

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

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

•°• (x - 1)(x + 3) are the factors of the given p(x)

To find zeros, let

p(x) = (x - 1)(x + 3) = 0

Then,

p(x) = (x - 1) = 0

•°• x = 1

And

p(x) = (x + 3) = 0

•°• x = -3

Thus, 1 and -3 are the zeroes of the given p(x).

Answer 2

Step-by-step explanation:

$p(x) = {x}^{2} - 2x - 3 \\ p(x) = {x}^{2} + 3x - x - 3 \\ p(x) = x(x + 3) - 1(x + 3) \\ p(x) = (x + 3)(x - 1) \\ either \: x + 3 = 0 \: or \: x - 1 = 0 \\ x = - 3 \\ x= 1 \\ thus \: - 3 \: and \: 1 \: are \: zroes \: of \: the \: given \: p(x).$