Published by: **Divyanshu Nay****ak**

In algebra, a quadratic equation (from the Latin quadratus for “square”) is an equation that can be rearranged in standard form as

*ax***²**+*bx*+*c*=0

### x=(-b±√(b²-4ac))/2a

where x represents an unknown, and **a**, **b**, and **c** represent known numbers, where a** ≠ 0**. If **a = 0**, then the equation is linear, not quadratic, as there is no * ax²* term. The numbers

**a, b,**and

**c**are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.

Let’s take a look at a couple of examples. Note that it is assumed that you can do the factoring at this point and so we won’t be giving any details on the factoring. If you need a review of factoring you should go back and take a look at the Factoring section of the previous chapter.

** Example ** Solve each of the following equations by factoring.

*x²−x=12**x²+40=−14x**y²+12y+36=0**4m²−1=0**3x²=2x+8**10z²+19z+6=0**5x²=2x*

Let us find roots of the equations with minimum calculation and

**WITHOUT PEN AND PAPER**.

Before we begin I’d like to share a few short tricks to find out the roots of any given equation. by looking at the signs of the equation we can determine the sign of the roots

let us take *ax***²**+*bx*+*c*=0 as our general equation.

In the first case, we have **to look at the sign of the consta**** nt **if the constant has ‘+’ sign just before itself then both the roots will have similar signs, such as with both roots are positive or both roots are negative. in the second step to decide the sign of roots, we will have to look at the second sign. both the signs of the roots will be opposite

Example: *ax*²+*bx*+*c*=0 has ‘ + + ‘ so the roots will be ‘ *-x1 – x2* ‘

in the other hand*ax*²-*bx*+*c*=0 here roots will have ” +*x1 + x2 * “

In the second case if the constant has **‘ – ‘** sign just before it then both roots will have **opposite signs**. but the value of the **greater number** depends upon the **first sign**. If the first sign is **Positive** then the **negative root** will have a **higher coefficient** similarly If the first sign is negative then the positive root will have a higher coefficient

Example:- ** ax²+bx–c=0 ** will have roots

*and*

**+x****where the coefficient of**

*-x**x will be greater*

**–**similarly,

** ax²-bx–c=0** will have roots

**and**

*+x***where the coefficient of**

*-x***will be greater**

*+x***To Summerize **

*ax*²+*bx*+*c*=0 → *-x and -x*

*ax*²-*bx*+*c*=0 → **+**x and +x

*ax*²+*bx*–*c*=0 → **+**x and -x**↑**

** ax²-bx–c=0** →

*+x*↑*and -x***↑ indicates the coefficient value is greater**

Numerical Ability or Quantitative Aptitude Section has given the opportunity to the aspirants when they appear for a banking examination. As the level of every other section is only getting complex and convoluted, there is no doubt that this section, too, makes your blood run cold. The questions asked in this section are calculative and very time-consuming. But once dealt with proper strategy, speed, and accuracy, this section can get you the maximum marks in the examination. Following is the Quantitative Aptitude quiz to help you practice with the best of latest pattern question

**Click here to download practice Questions**