Question

Please answer these three questions please!

Answer 1

6) OPTION C

7) OPTION D

8) X = -3, -4

Explanation:

6) To determine the roots of a function from the graph, look at the point where it cuts the x- axis.

In this graph, we see that it cuts the x - axis at x = -3 and x = 4.

That means, they are the roots of the equation. OPTION C is the answer.

7) Completing the square means to add and subtract a number, so that it can written in the form
`$ (a + b)^2 $`.

Here, the expression is:
`$ x^2 - 2x $`.

We know the formula is:
`$ (a + b)^2 = a^2 + 2 a . b + b^2 $`

Comparing with the expression, we have:

a² = x² ⇒ a = x

2ab = 2. x

This is equivalent to 2 . 1. x

Therefore, b = 1

So, we can add and subtract 1 to complete the square.

8) x² + 7x + 12

It is quadratic equation.

The formula to solve an equation of this type:

ax² + bx + c = 0, x =
`$ (- b \pm √(b^2 - 4ac))/(2a) $`

Using the formula here, we get:

x =
`$ (- 7 \pm √(49 - 4(1)(12)))/(2(1)) $`

`$ \implies x = (- 7 \pm √(49 - 48))/(2) $`

`$ \implies x = (- 7 \pm 1)/(2) $`

So, x takes two values, viz.,

`$ x = (-7 - 1)/(2) $` ;
`$ x = (-7 + 1 )/(2) $`

`$ \implies x = (-8)/(2) $` ;
`$ \implies x = (- 6)/(2) $`

∴ x = -3; x = - 4 are the two roots of the equation.