MULTIPLE CHOICE Which of the following is a solution of the...

MULTIPLE CHOICE Which of the following is a solution of the equation $2 x^{2}+8 x-25=5 ?$ \begin{array}{ccccc}\mathbf{A} & \sqrt{17}+1 & \mathbf{B} & -\sqrt{19}-2 & \mathbf{C} & \sqrt{17}-2 & \mathbf{D} &\sqrt{21} & -2\end{array}

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Quadratic Equation

A quadratic equation is a polynomial equation of degree two, meaning that the highest exponent of the variable is two. These equations can have two real roots, one repeated real root, or two complex roots, and they are fundamental in algebra and are solved using various methods such as factoring, completing the square, or the quadratic formula.

Rearranging Equations

Rearranging equations involves moving all terms to one side of the equation to set it equal to zero. This step is essential in solving quadratic equations because it puts the equation into standard form, which is necessary for applying methods like factoring or the quadratic formula.

Quadratic Formula

The quadratic formula provides a direct method to solve any quadratic equation expressed in the standard form ax² + bx + c = 0. It states that the solutions for x can be found using the formula x = (-b ± ?(b² - 4ac)) / (2a). This method is especially useful when the equation does not factor neatly.

Discriminant

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature of the roots of the quadratic equation: if the discriminant is positive, the equation has two distinct real roots; if zero, one real repeated root; and if negative, two complex conjugate roots.

Transcript

Please give Ace some feedback