Being a banking aspirant, we know that you get nightmares when you think about solving Quantitative Aptitude questions accurately and in the given time. Quant section is difficult because questions in this section are very calculative and lengthy and on the actual exam day, you will have to solve the questions usually within less than a minute. Aspirants preparing for **exams like SBI Clerk, SBI PO, LIC AAA, IBPS PO, IBPS Clerk** concentrate more on this section as speed and accuracy matters in this section.

One important topic which most of the students find difficult is the Quadratic Equations. You must be aware that, in exams like SBI Clerk prelims, SBI Clerk Mains, SBI PO Prelims, SBI PO Mains, IBPS PO Prelims, usually at least 5 questions are asked from this chapter.

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## ixamBee’s expert has come up with short cut tricks which will help in solving Quadratic Equation Questions quickly with accuracy.

### Quadratic equations are of form: **ax**^{2}**+bx+c = 0**

^{2}

Here the highest power of x is 2 so here there will be always two roots of x.

When any question asked in exam then there will be 2 equations given, one in x & second in y. You have to find a relation between x & y and Mark answer accordingly:

- If x > y
- If x < y
- If x ≥ y
- If x ≤ y
- If x = y or relationship between x & y is not established.

Note: – Relationship is not established between x & y if x> y & also x<y at same time.

**Rule 1:**

If the given equation is **a****x ^{2}+bx+c = 0** (means when a, b & c all are ‘+’),

**then both of its roots will always be**

**Negative.**

**Rule 2:**

If the given equation is** ****a****x ^{2}– bx+c = 0** (means when only b is ‘-’),

**then both of its roots will always be**

**Positive.**

**Rule 3:**

If the given equation is **none from the above 2 rules,** then **one root will be always ****Positive**** and other will be always**** Negative****.**

### **TRICK 1:**

**If one equation of x is from rule 1 & other equation of y is from rule 2 then answer will be always x<y**

** ****Example 1:**

- 3x
^{2}+5x+2 = 0 - 3y
^{2}-7y +4 = 0

**Solution:**

Here you need not to solve the whole equations.

Signs of both roots of x will be negative because of rule I

& signs of both roots of y will positive because of rule 2.

Hence x<y.

** Practice free mock tests for SBI PO Prelims **

**Example 2:**

- 7x
^{2}-23x+6 = 0 - 8y
^{2}+18y +4 = 0

**Solution:**

Here again you need not to solve the whole equations.

Signs of both roots of x will be positive because of rule 2

& signs of both roots of y will negative because of rule 1.

Hence x>y.

**TRICK II:**

If both the equations of x & y are from rule 3 (means it is **neither** **ax ^{2}+bx+c = 0 nor ax**

^{2 }**–bx + c =0**), so roots of both are positive as well as negative, then in that case,

**there will be always no relationship between x & y.**

**Example 3:**

- 7x
^{2 }– 23x – 20 = 0 - 8y
^{2}+14y – 4 = 0

**Solution:**

You again need not to solve the whole equations here.

Signs of both roots of x will positive as well as negative, because of Rule 3.

Signs of both roots of y will positive as well as negative, because of Rule 3.

So here no relationship between x & y can be established.

**These 2 key points will help you to solve at least 1 to 2 questions in every 5 question asked in any banking exam.**

**Example: Find the relation between x & y and mark the answer accordingly.**

**3x**^{2}+13x +12 = 0**4y**^{2}-17y -15= 0- If x > y
- If x < y
- If x ≥ y
- If x ≤ y
- If x = y or relationship between x & y is not established.

**Solution: –**

**Conventional method to solve any quadratic equation:-**

**3x ^{2} +13x +12 = 0**

**3x ^{2} +4x +9x+12 = 0**

**x(3x+4)+3(3x+4) = 0**

**(x+3)(3x+4) = 0**

**So x = -3, -4/3**

**Smart Way to solve this**

**Step I: Find pairs of splitting middle terms**

**Step II: Change the signs**

**Step III: Just divide by ‘a’ (coefficient of x ^{2}) to find the final answer**

**So Pairs are = 9, 4**

**Values after changing the signs = -9, -4**

**Final value of x dividing by 3 = -3, -4/3**** **

**Let’s solve also another equation, 4y ^{2} -17y -15= 0**

**So pairs are = 3, -20**

**Values after changing the signs = -3, 20**

**The final value of y dividing by 4 = -3/4, 5**

**After finding the roots of x &y, we can easily compare the relationship between x & y.**

**So here x<y.**

**Practice Free Mock Tests for SBI Clerk Prelims**

You have seen how Quadratic equation questions can be easily solved by these tricks so practice at least 150Q of this chapter to be master in it.

ixamBee has started Quantitative Aptitude Short Cut Tricks Series, where we will be posting short cut tricks on every topic in Quantitative Aptitude every Thursday.

**Stay Tuned & Practice hard for more tricks!!!!!!!!!**

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