• Math

  What is meant by Quadratic Equation?

  Posted by Rupali Gadekar on May 12, 2021 at 9:12 am

  What is meant by Quadratic Equation?

  • This discussion was modified 3 years, 5 months ago by  Kidpid.

  Aashutosh replied 3 years, 5 months ago 2 Members · 1 Reply
• 1 Reply

• 

  Aashutosh

  Member

  May 12, 2021 at 2:01 pm

  Helpful

  Up

  1

  Down

  Not Helpful

  ::

  Quadratic Functions:

  Quadratic functions involve the second power of the variable but no higher power. The kinetic energy of a moving body is given by K.E. =1/2mv^2 , where m represents the mass and v represents the velocity of the object.

  In general, A quadratic function is function that may be defined by the equation y=ax^2+bx+c, where a, b, and c are complex numbers constants or parameters, but a≠0. Notice that the restriction a≠0 assures that y=ax^2+bx+c defines a non-linear function.

  The following equations define the quadratic functions:

  1. y=x^2

  2. y=-4x^2

  3 y=x^2-6x+8

  Quadratic Equations:

  An equation in which the highest power of the variable i.e., degree is two is called a quadratic equation.

  ax^2+bx+c=0, where a,b,c are constants, is a general quadratic equation.

  Examples:

  1. 5x^2+2x=0

  2. x^2+2x-1=0

  3. 58x^2+52x +6=0

  4. 9x^2+6x-1=0

  Consider the quadratic equations ax^2+bx+c=0, where a, b, c € R and a≠0

  Roots of the equation is given by x=(-b±√(b^2-4ac))/2a .

  What is plus/minus sign?

  The plus/minus sign is used because every quadratic equation has maximum two solution.

  Nature of Roots:

  The nature of the roots, real or imaginary, depends on the b^2-4ac.

  This is generally denoted by D also called Discriminant.

  1. If D=0, Roots are real and equal.

  2. If D>0, Roots are real and distinct.

  3. If D<0, Roots are imaginary.

Log In to Reply