Formula for Quadratic Equation Problems

Formula For Quadratic Equation Problems

A Quadratic Equation is the equation that can be rearranged in standard form ax2 + bx + c = 0 as where x is a variable and a, b, and c represent constants , where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no term.

Formulas of quadratic equations

Formulas for Quadratic Equations & Definitions

  • An equation where the highest exponent of the variable is a square. Standard form of quadratic equation is ax2+bx+c = 0
  • Where,  x is the unknown variable and a, b, c are the numerical coefficients.

Quadratic Equations Formulas

  • If ax2+bx+c = 0 is a quadratic equation, then the value of x is given by the following formula
  • x = \frac{-b  \pm  \sqrt{b^2 – 4ac}}{2a}

Formulas of Quadratic Equations & Method to Solve Quadratic Questions

  • Factorization 

It is very simple method to to solve quadratic equations. Factorization give 2 linear equations
For example:    x2 + 3x – 4 = 0

      Here, a = 1, b = 3 and c = -4

      Now, find two numbers whose product is – 4 and sum is 3.

      So, the numbers are 4 and -1.

     Therefore, two factors will be 4 and -1

Completing the Square Method

  • Every Quadratic question has always a square term. If we could get two square terms of quality sign we can get a linear equations. Middle term is called as ‘b’ and splited by (\frac{b}{2})^2

For example :  – x²+ 6x +7

    Here x² =1, b= 4

    (\frac{b}{2})^2 = (\frac{4}{2})^2 = 4

x²+4x+4 = -1+4

(x+2)² = 3

Take the square of both side

x+2 = ±\sqrt{3} = ± 1.73

Therefore, x = -0.27 or -3.73

Formulas of Quadratic Equations & Key points to Remember

Other basic concepts to remember while solving quadratic equations are:

1.Nature of roots

    • Nature of roots determine whether the given roots of the equation are real, imaginary, rational or irrational. The basic formula is b² – 4ac.
    • This formula is also called discriminant or D. The nature of the roots depends on the value of D. Conditions to determine the nature of the roots are:
    • If D < 0, than the given roots are imaginary.
    • If D = 0, then roots given are real and equal.
    • If D > 0, then roots are real and unequal.
    • Also, in case of D > 0, if the equation is a perfect square than the given roots are rational, or else they are irrational.

2. Sum and product of the roots

    • For any given equation the sum of the roots will always be  – \frac{b}{a} , and the product of the roots will be  – \frac{c}{a} . Thus, the standard quadratic equation can also be written as x2 – (Α + Β)x + Α*Β = 0

3. Forming a quadratic equation

    • The equation can be formed when the roots of the equation are given or the product and sum of the roots are given.

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