Answer to Question #227916 in Algebra for Val

Question

1.1 Using graphical method, solve the equation; 𝑥

2

- 3𝑥 – 4 = 0

1.2 Solve the equation; x

2

- 8x + 7 = 0 using the Quadratic Formula

Answer 1

1.1 Using graphical method, let solve the equation $𝑥^2- 3𝑥 -4 = 0.$

Let us sketch the graph of the function $f(x)=𝑥^2- 3𝑥 -4:$

It follows from the graph that the solutions of the equation $𝑥^2- 3𝑥 -4 = 0$ are $x=-1$ and $x=4.$

1.2 Let us solve the equation $x^2- 8x + 7 = 0$ using the Quadratic Formula.

Let us find the discriminant:

$D=(-8)^2-4\cdot 7=64-28=36$

We conclude that the solutions are

$x_1=\frac{8+\sqrt{36}}{2}=\frac{8+6}{2}=\frac{14}{2}=7$ and $x_2=\frac{8-\sqrt{36}}{2}=\frac{8-6}{2}=\frac{2}{2}=1.$