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### Expert Maths Tutoring in the UK ^{[1]}

What are the solutions of the quadratic equation 0 = -x2 – 6x – 8?. A quadratic equation is an algebraic expression of the second degree in x.

\(x=\frac{-(-6)\pm \sqrt{(-6)^{2}-4(-1)(-8)}}{2(-1)}\\x=\frac{6\pm \sqrt{36-32}}{-2}\\x=\frac{6\pm \sqrt{4}}{-2}\\x=\frac{6\pm 2}{-2}\). Therefore, the solutions of the quadratic equation are x = -2 and x = -4.

The solutions of the quadratic equation 0 = -x2 – 6x – 8 are x = -2 and x = -4.

### What is the discriminant of #x^2+2x+8=0# and what does that mean? ^{[2]}

What is the discriminant of #x^2+2x+8=0# and what does that mean?. The discriminant is the portion of the quadratic formula for solving a quadratic equation:

### Solve Using the Quadratic Formula x^2-2x-8=0 ^{[3]}

Substitute the values , , and into the quadratic formula and solve for .. Pull terms out from under the radical, assuming positive real numbers.

### Microsoft Math Solver ^{[4]}

First, the expression needs to be rewritten as x^{2}+ax+bx-8. Since ab is negative, a and b have the opposite signs

Rewrite x^{2}-2x-8 as \left(x^{2}-4x\right)+\left(2x-8\right).. Factor out x in the first and 2 in the second group.

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.. x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-8\right)}}{2}

### Solve Quadratic equations x^2-2x+8=0 Tiger Algebra Solver ^{[5]}

Step-1 : Multiply the coefficient of the first term by the constant 1 • 8 = 8. Step-2 : Find two factors of 8 whose sum equals the coefficient of the middle term, which is -2 .

Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting “y” because the coefficient of the first term, 1 , is positive (greater than zero).

Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

### Why are there four solutions to $x^2-2x-8=0$ in $\mathbb{R}$? Or am I wrong? ^{[6]}

It might be a very trivial question to ask but why do we get four different solutions for a quadratic equation using these two methods?. We see that factors are $(x-4)$ and $(x+2)$ so we get $x=4$ or $- 2$.

### [Solved] The equation x2 ^{[7]}

As we know, the sum of roots = \(-b\over a\) and, the product of roots = \(c\over a\). Since the product of the roots is negative ⇒ one of the roots is positive and the other is negative.

So, The equation x2 – 2x – 8 =0 will have the numerically larger root as positive.. For a quadratic equation of the form, ax2 + bx + c = 0, we can use the following table to determine the sign of the roots of the equation.

|- ve||+ ve||The numerically larger root is positive and the other root is negative.|. |- ve||-ve||The numerically larger root is negative and the other root is positive.|

### See how to solve it at QANDA ^{[8]}

$x = \dfrac { – \left ( – 2 \right ) \pm \sqrt{ \left ( – 2 \right ) ^ { 2 } – 4 \times 1 \times \left ( – 8 \right ) } } { 2 \times 1 }$. $x = \dfrac { 2 \pm \sqrt{ \left ( – 2 \right ) ^ { 2 } – 4 \times 1 \times \left ( – 8 \right ) } } { 2 \times 1 }$

$ $ Remove negative signs because negative numbers raised to even powers are positive $ $. $x = \dfrac { 2 \pm \sqrt{ 2 ^ { 2 } – 4 \times 1 \times \left ( – 8 \right ) } } { 2 \times 1 }$

$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $. $ $ Multiplying any number by 1 does not change the value $ $

### 1. What is the solution set for x^2 + 2x – 8 0 2. What is solution set for -x^2 + 2x -3 3. Graph 2x^2 3 – 5x ^{[9]}

The solution to an inequality in one variable may be determined by finding the critical points (zeros and singularities) of the associated equation which equals zero. These points will divide the domain into regions to be checked for solving the inequality.

{eq}y = x^2 + 2x – 8 > 0 \\ y = (x+4)(x-2) > 0 {/eq}. Learn the steps for how to solve a quadratic inequality and how to find the solution set of quadratic inequalities.

### Sources

- https://www.cuemath.com/questions/what-are-the-solutions-of-the-quadratic-equation-0-x2-6x-8/#:~:text=Summary%3A-,The%20solutions%20of%20the%20quadratic%20equation%200%20%3D%20%2Dx2%20%2D,2%20and%20x%20%3D%20%2D4.
- https://socratic.org/questions/what-is-the-discriminant-of-x-2-2x-8-0-and-what-does-that-mean#:~:text=Jul%2015%2C%202015-,The%20discriminant%20of%20×2%2B2x%2B8%3D0,equation%20has%20no%20Real%20solutions.
- https://www.mathway.com/popular-problems/Algebra/200343
- https://mathsolver.microsoft.com/en/solve-problem/%7B%20x%20%20%7D%5E%7B%202%20%20%7D%20%20-2x-8
- https://www.tiger-algebra.com/drill/x~2-2x_8=0/
- https://math.stackexchange.com/questions/1217750/why-are-there-four-solutions-to-x2-2x-8-0-in-mathbbr-or-am-i-wrong
- https://testbook.com/question-answer/the-equation-x2-2x-8-0-will-have–60511414821aaf2e0d9f3e54
- https://qanda.ai/en/search/x%20%5E%7B%202%20%20%7D%20%20-2x-8%20%3D%20%200?search_mode=expression
- https://homework.study.com/explanation/1-what-is-the-solution-set-for-x-2-plus-2x-8-0-2-what-is-solution-set-for-x-2-plus-2x-3-3-graph-2x-2-3-5x.html