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Activity Discussion Math What is meant by Quadratic Equation?

  • What is meant by Quadratic Equation?

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

    What is meant by Quadratic Equation?

    • This discussion was modified 1 year, 6 months ago by  Kidpid.
    Aashutosh replied 1 year, 6 months ago 2 Members · 1 Reply
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  • Aashutosh

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    May 12, 2021 at 2:01 pm
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    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.

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