Quadratic Equation: Meaning of a Quadratic Equation, Sum and Product of Roots of a Quadratic Equation (For CBSE, ICSE, IAS, NET, NRA 2022)

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Quadratic Equation

  • A quadratic equation can be defined as the polynomial equation with two as the highest degree.
  • Quadratic equation may also be called as univariate since the quadratic include only one unknown term or variable.
  • There will be solutions for the equation since quadratics have a degree equal to two.

This equation can be expressed in the form of

… (i)

Here x is the unknown variable and a, b and c are the constant terms.

The roots of the equation in (i) will be:

… (ii)

There will be two solutions for x and the same is being indicated by the plus/minus signs.

is the discriminant of the equation and the same can be denoted by D or

Using (ii) We have,

If and represent the roots of the above equation, then the relationship between the roots of quadratic equation and the coefficients a, b and c can be represented as:

Sum of roots and roduct of roots

Proof of Quadratic Equation

On squaring both sides, we get

Applications of Quadratic Equation

  • For solving problems related in finding out area of rectangle, parallelogram and so on.
  • It is also useful in solving word problems involving Distance, speed, and time, etc.

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