Answer:
6) OPTION C
7) OPTION D
8) X = -3, -4
Step-by-step 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 [tex]$ (a + b)^2 $[/tex].
Here, the expression is: [tex]$ x^2 - 2x $[/tex].
We know the formula is: [tex]$ (a + b)^2 = a^2 + 2 a . b + b^2 $[/tex]
Comparing with the expression, we have:
a² = x² ⇒ a = x
2ab = 2. x
This is equivalent to 2 . 1. x
Therefore, b = 1
So, we can add and subtract 1 to complete the square.
8) x² + 7x + 12
It is quadratic equation.
The formula to solve an equation of this type:
ax² + bx + c = 0, x = [tex]$ \frac{- b \pm \sqrt{b^2 - 4ac}}{2a} $[/tex]
Using the formula here, we get:
x = [tex]$ \frac{- 7 \pm \sqrt{49 - 4(1)(12)}}{2(1)} $[/tex]
[tex]$ \implies x = \frac{- 7 \pm \sqrt{49 - 48}}{2} $[/tex]
[tex]$ \implies x = \frac{- 7 \pm 1}{2} $[/tex]
So, x takes two values, viz.,
[tex]$ x = \frac{-7 - 1}{2} $[/tex] ; [tex]$ x = \frac{-7 + 1 }{2} $[/tex]
[tex]$ \implies x = \frac{-8}{2} $[/tex] ; [tex]$ \implies x = \frac{- 6}{2} $[/tex]
∴ x = -3; x = - 4 are the two roots of the equation.
