Quadratic Equation Questions for RRB Clerk Exam, Download Free PDF

RRB Clerk is considered the most competitive among the other clerical-level exams, and hardly 35 days are left for the RRB Clerk 2025. In such a scenario, this is very important to practice each and every topic as much as you can. And especially topics like the quadratic equation demand ample time, and this is the right time to do the same. In this blog, we are discussing the step-by-step approach to solving the quadratic equation and what common mistakes you should avoid while doing the same. But before that, let’s understand the concept of a quadratic equation. 

Download Quadratic Equation Questions for RRB Clerk Exam

In this section, we are providing a PDF that contains Quadratic Equation Questions for the RRB Clerk exam. You can download the PDF and start your practice, as hardly a month is left. The PDF is curated by our experts after analysing the past year’s trends.

What is a Quadratic Equation?

 A Quadratic Equation is an equation of the form:

ax²+bx+c=0 where a, b, and c are constants, and a ≠ 0.

The solutions of this equation are called roots and can be found using the formula:

photo

Here, the value inside the square root (b² – 4ac) is known as the discriminant (D).

• If D > 0, the roots are real and distinct.
  
• If D = 0, the roots are real and equal.
  
• If D < 0, the roots are imaginary.

How to Solve Quadratic Equation Questions Quickly for RRB PO?

In this section, we are discussing about how to solve quadratic equations quickly in RRB PO Exams. We are using an example to explain each step to solve the question. We are taking two examples, one is easy to factorise, and the other is

Example pair A (easy to factor)

Equation 1: x²−8x+15=0

Equation 2: y²−9y+20=0

1. Factorise smartly

Look for two numbers whose product = c and sum = b. You just need to find the numbers, and by rigorous practice, it will become handy.

Equation 1: In equation 1, we want two numbers with a product of 15 and a sum of 8.
Candidates: 3 and 5. So

x²−8x+15=(x−3)(x−5)=0

Roots: x=3,  5.

Equation 2: product c = 20, sum b = 9.
Candidates: 4 and 5. So

y²−9y+20=(y−4)(y−5)=0

Roots: y=4,  5. 

2. Avoid using the formula every time

Use factorisation when integer pairs are formed. Using the quadratic formula can be slower and invites arithmetic errors. Only use the formula when factorising fails or when coefficients are messy.

From Example A, we used factorisation and got exact roots immediately, no square roots, no fraction arithmetic.

3. Compare systematically

When you have sets of solutions, compare all possible pairs to determine the relation.

For Example A:

• x can be 3 or 5.
  
• y can be 4 or 5.
  

Compare pairwise:

• If x=3 and y=4 → x<y.
• If x=3 and y=5 → x<y
• If x=5 and y=4 → x>y.
• If x=5 and y=5 → x=y

Since different comparisons give x<y,  x>y, and x=y, the only correct statement is that a relationship cannot be established uniquely (unless the question asks for something like whether x≤y is always true, check all pairs; here it is not always true). Always enumerate all root combinations quickly.

Shortcut for comparisons
If the smallest possible x is greater than the largest possible y, you can write x>y immediately. If ranges overlap, you must check combinations.

Common Mistakes to Avoid While Solving the Quadratic Equation for RRB PO Exam

In this section, we are discussing the mistakes that students generally commit while solving the quadratic Equation. 

• Many aspirants forget to check positive and negative signs while factorising. For example, in x²−2x−15=0, some take 3 and 5 as factors, but the correct pair is −5 and 3 since (−5)×3=−15 and (−5)+3=−2. Always verify the sum and product with proper signs before finalising factors.
• In quadratic comparison questions, students often compare only one pair of roots. For instance, if x=3,4 and y=4,5, you must compare all combinations before concluding. Since one pair gives equality and the others x<y, the correct answer is x≤y. Always check every possible pair of x and y values.
• Equations like 4x²−12x+8=0 should first be simplified to x²−3x+2=0. Simplifying reduces errors and makes factorisation faster. Avoid jumping directly to the quadratic formula before checking for common factors.
• RRB Clerk exams are time-bound. Spending too long on one question can lead to wastage of time and hence will affect productivity. If you can’t solve within 1–1.5 minutes, skip and return later. Use discriminant checks or approximations for quick decisions.

Conclusion

In this article, we have provided the steps along with an example to solve a quadratic equation in RRB PO Exams. To practice more such questions, you can buy our test series, where you can get to reattempt the full-length mock tests and get a Detailed Comparison with the Topper, compare your Time, Score, Accuracy, Correct/Wrong Answers, and even the Average Performance side-by-side.

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