Question

Draw the graph of quadratic polynomial
P(x) = x^{2} - x - 2
and write the
solution

Answer 1

EXPLANATION.

Graph of the quadratic equation.

⇒ p(x) = x² - x - 2.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ p(x) = x² - 2x + x - 2.

⇒ p(x) = x(x - 2) + 1(x - 2).

⇒ p(x) = (x + 1)(x - 2).

Zeroes of the equation.

⇒ (x + 1)(x - 2) = 0.

⇒ x = -1 and x = 2.

Put the value of x in equation, we get.

⇒ p(x) = x² - x - 2.

Put the value of x = -1 in equation, we get.

⇒ y = (-1)² - (-1) - 2.

⇒ y = 1 + 1 - 2.

⇒ y = 2 - 2.

⇒ y = 0.

Their Co-ordinates = (-1,0).

Put the value of x = 2 in equation, we get.

⇒ y = (2)² - (2) - 2.

⇒ y = 4 - 2 - 2.

⇒ y = 4 - 4.

⇒ y = 0.

Their Co-ordinates = (2,0).

Put the value of x = 0 in equation, we get.

⇒ y = (0)² - (0) - 2.

⇒ y = -2.

Their Co-ordinates = (0,-2).

Answer 2

Answer:

Given :-

$\bf \: x^{2} - x - 2$

To Find :-

Solution

Solution :-

At first we need to factorise

P(x) = x² - x - 2

P(x) = x² - (2x - x) - 2

P(x) = x² - 2x - x - 2

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

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

Either,

x = 0 - 1

x = - 1

or

x = 0 + 2

x = 2

When x = -1

(-1)² - (-1) - 2

(1) + 1 - 2

2 - 2

0

Coordinate = (-1,0)

When x = 2

(2)² - 2 - 2

4 - 2 - 2

2 - 2

0

Coordinate = (2,0)

Therefore,

x = 0

(0)² - 0 - 2

0 - 0 - 2

0 - 2

- 2

Coordinates = (0,-2)