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Quadratic equation is one of the most important and potentially high-scoring topics asked in different banking and insurance exams, such as IBPS PO, SBI PO, SBI Clerk, IBPS Clerk, RRB Assistant, RRB Scale 1, LIC Assistant, LIC AAO, etc. You can expect a set of 5 questions on this topic in the prelims of every banking and insurance examination. Achieving proficiency in this topic demands keen observational skills. Nonetheless, with dedicated practice, you can attain mastery and achieve a perfect score in this area. Smartkeeda offers a diverse range of Quadratic Equation questions with solutions to facilitate effective practice and enhance your prospects of achieving a high score.

A quadratic equation, denoted by the variable x, takes the form of ax2 + bx + c = 0, where a, b, and c represent real numbers, with a ≠ 0. For instance, 2x2 + x - 300 = 0 is a quadratic equation. However, to establish the standard representation of this equation, we arrange the terms of p(x) in descending order of their degrees, resulting in ax2 + bx + c = 0, with a ≠ 0. This particular form, ax2 + bx + c = 0, where 'a' is not equal to zero, is referred to as the standard form of a quadratic equation.

Also known as the Sridharacharya formula, the quadratic formula is a formula that provides the two solutions to a quadratic equation. The Quadratic formula stands as the most straightforward method for determining the roots of a quadratic equation. In cases where certain quadratic equations resist easy factorization, the Quadratic formula offers a convenient and efficient means to swiftly calculate the roots.

The Quadratic Formula is a rule that says that, in any equation of the form ax2 + bx + c = 0, the solution x-values of the equation are given by:

Example

Solve using Quadratic formula 2x2 - 7x + 3 = 0
Solution:
Comparing the equation with the general form ax2 + bx + c = 0 gives,
a = 2, b = -7, and c = 3
Now, calculate the discriminant (b2 - 4ac):
b2 - 4ac = (-7)2 - 4 * 2 * 3 = 49 - 24 = 25
Now, substitute the values into the quadratic formula:

x1 = (-b + √(b2 - 4ac)) / (2a)
x1 = (-(-7) + √25) / (2 * 2)
x1 = (7 + 5) / 4 = 3

x2 = (-b - √(b2 - 4ac)) / (2a)
x2 = (-(-7) - √25) / (2 * 2)
x2 = (7 - 5) / 4 = 1/2

So, the roots of the equation 2x2- 7x + 3 = 0 are x1 = 3 and x2 = 1/2.

Factoring quadratics is a technique used to represent the quadratic equation ax^2 + bx + c = 0 as a multiplication of its linear factors in the form (x - p) (x - q), where p and q represent the roots of the quadratic equation ax^2 + bx + c = 0.

Factoring Techniques

Quadratic equations can be factorized through various methods such as

• Splitting the middle term,
• Using quadratic formula or Shridharacharya formula
• Completing the square or square root method

Bank exams often include these types of Quadratic Equation questions to assess candidates' problem-solving skills and their ability to discern relationships between variables, making it a critical component of the quantitative section. Questions on Quadratic Equations are asked in the form of inequalities in the Quantitative Aptitude section. Generally, two quadratic equations in two different variables are given. You have to solve both of the Quadratic equations to get to know the relation between both variables.

Suppose we have two variables ‘x’ and ‘y’. The relationship between the variables can be any one of the following:

x > y
x < y
x = y or relation can’t be established between x & y
x ≥ y
x ≤ y

Practice Exercises

I.   x2 – 25x + 114 = 0
II.  y2 – 10y + 24 = 0

1. if x > y
2. if x < y
3. if x ≥ y
4. if x ≤ y
5. if x = y or relationship between x and y can't be established
Correct Option: C

I. x2 – 25x + 114 = 0

x2 – 19x – 6x + 114 = 0

(x  6)(x  19) = 0

x = 19 or x = 6

II. y2 – 10y + 24 = 0

y2 – 6y – 4y + 24 = 0

(y  4)(y  6) = 0

y = 6 or y = 4

When x = 19, x > y

When x = 6, x ≥ y

Hence, x ≥ y

Hence, option C is correct.

### Tips for Efficient Quadratic Equation Solving

When solving quadratic equations, it's important to keep the following points in mind to ensure accurate and efficient problem-solving:

• Recognize that a quadratic equation is in the form ax^2 + bx + c = 0
• After finding potential solutions, ensure they satisfy the original equation.
• Carefully handle the signs (+/-) in the quadratic formula to avoid calculation errors.
• Observe carefully while comparing the roots of given equations
Regular practice is key to improving your proficiency in solving quadratic equations efficiently. Smartkeeda offers a wealth of free resources and materials for Quadratic equations, providing invaluable assistance to help you excel in mastering this topic in the easiest manner possible. You can visit our website to practice free Quadratic Equation Questions Now!