25x² - 36 = 0
  25x² - 30x + 30x - 36 = 0
5x(5x) - 5x(6) + 6(5x) - 6(6) = 0
  5x(5x - 6) + 6(5x - 6) = 0
(5x + 6)(5x - 6) = 0
5x + 6 = 0 or 5x - 6 = 0
   - 6 - 6 + 6 + 6
5x = -6   5x = 6
5 5 5   5
x = -1.2 x = 1.2

6 0

3 years ago

2. Using Vièta's theorem, find the solutions to the equation. a) x^2 - 3x + 2 = 0 b) x^2 + 2x - 15 = 0.

olga_2 [115]

Given:

$\begin{gathered} x^2-3x+2=0 \\ x^2+2x-15=0 \end{gathered}$

Required:

We need to find the solution by Vièta's theorem.

Explanation:

Compare 1st equation with

$ax^2+bx+c=0$

we get

$\begin{gathered} a=1 \\ b=-3 \\ c=2 \end{gathered}$

Vièta's theorem is

$\begin{gathered} x_1+x_2=-\frac{b}{a} \\ x_1x_2=\frac{c}{a} \end{gathered}$

$\begin{gathered} x_1+x_2=3 \\ x_1x_2=2 \end{gathered}$

now solve this equation and we get

$\begin{gathered} x_1=1 \\ x_2=2 \end{gathered}$

because addition of 1 and 2 is 3 and multiplication is 2

Now for 2nd equation

$\begin{gathered} a=1 \\ b=2 \\ c=-15 \end{gathered}$

apply Vièta's theorem

$\begin{gathered} x_1+x_2=-2 \\ x_1x_2=-15 \end{gathered}$

by this

$\begin{gathered} x_1=3 \\ x_2=-5 \end{gathered}$

because addition of 3 and -5 is -2 and multiplication is -15

8 0

1 year ago

Please help me what is incorrect about this problem

Effectus [21]

Answer:

The answer is correct

Step-by-step explanation:

6 0

3 years ago

For what real values of $c$ is $x^2 + 16x + c$ the square of a binomial? if you find more than one, then list your values separa

s2008m [1.1K]

The Square of a Binomial is always a trinomial. In general, you have the following relationship for a square binomial:

$(a+b)^2=a^2+2ab+b^2$

The trinomial of our problem is:

$x^2+16x+c$

So we need to find the real value of $c$ such that this is a square of a binomial. Matching the general form with the trinomial of our problem we have the following equations:

 $a=x \\ 2ab=16x = 2(x)(8) \\ where \ b=8 \\ \\b^2=c \therefore c=8^2 \therefore \boxed{c=64}$

Therefore the square of our binomial is:

 $(x+8)^2=x^2+16x+64$

4 0

3 years ago