quadratic equations

• Quadratic equations are equations in the form ax2 + bx + c = 0 where a, b, and c are real numbers and a is not equal to 0.

  Simply put, a quadratic equation has two as the highest exponent of its variable. For example, x2 + 4x + 4 = 0 is a quadratic equation since the highest exponent of the variable in this equation is 2.
• The standard form of a quadratic equation is ax2 + bx + c = 0
• ax2 = c or ax2 + c = 0 Form.
• The solutions of a quadratic equation are also called the roots of a quadratic equation. Thus, when we say the roots of x2 = 9, we refer to the solution of x2 = 9.
• If you use square root, always keep in mind to use negative and positive signs
• solve for x

  A) x=-3+sq2 and x=-3-sq2

  
• Quadratic formula

  A) -b+-sqb2-4ac/2a

  
• The discriminant of a quadratic equation allows you to determine the “nature of the roots” of a quadratic equation without actually solving it.
• When we say “nature of the roots,” we are referring to three things:

  1. The signs of the roots;
  2. Whether the roots are real or complex numbers; and
  3. Whether the roots are identical or not.

  Through the discriminant, we can determine if a quadratic equation will give us roots that are real numbers or complex numbers, as well as if they are positive or negative numbers. We can also determine if that equation’s roots are identical.
• discriminant formula

  A) b2-4ac

  
• What does the discriminant tell us?

  • If the computed value of the discriminant is positive (D > 0), then the quadratic equation has two real distinct roots (or two real different roots).
  • If the computed value of the discriminant is 0 (D = 0), then the quadratic equation has two identical real roots (or has only one repeated root).
  • If the computed value of the discriminant is negative (D < 0), then the quadratic equation has no real roots. This means that the roots of the quadratic equation are complex numbers.
• sum and product of roots

  A) -b/a

  B) c/a

  
• perimeter of a rectangle is defined as P = 2l + 2w
•  area of a rectangle is defined as A = l ⋅ w.