16 questions from actual SSC GD Constable papers · all shown free · click option to reveal solution
Quadratic Equations are polynomial equations with the highest degree of 2. They form the backbone of algebra questions in SSC CGL and appear in almost every exam paper. A quadratic equation has the standard form ax² + bx + c = 0, where 'a' cannot be zero. Core Properties and Rules:
Every quadratic equation has exactly two roots (solutions). These roots can be real and equal, real and unequal, or imaginary. The nature of roots depends on the discriminant (b² - 4ac). When discriminant > 0, roots are real and unequal. When discriminant = 0, roots are real and equal. When discriminant < 0, roots are imaginary.
SSC CGL typically asks 2-3 questions on quadratic equations. Common question types include finding roots, determining nature of roots, forming equations from given roots, and word problems leading to quadratic equations. Questions often involve finding maximum/minimum values or solving practical problems.
#1 - Middle Term Splitting: For ax² + bx + c = 0, find two numbers whose product = ac and sum = b. Split the middle term using these numbers. This method is faster than the quadratic formula for most SSC questions. Shortcut Trick #2 - Perfect Square Recognition: If b² = 4ac, the equation is a perfect square.
The root is -b/2a (repeated twice). This saves calculation time.
Identify a = 2, b = -7, c = 3
Find ac = 2 × 3 = 6
Find two numbers whose product = 6 and sum = -7 These are -6 and -1 (since -6 × -1 = 6 and -6 + (-1) = -7)
Rewrite: 2x² - 6x - x + 3 = 0
Factor: 2x(x - 3) - 1(x - 3) = 0
(2x - 1)(x - 3) = 0
Roots are x = 1/2 and x = 3 Worked Example 2: Find the equation whose roots are 3 and -2.
Sum of roots = 3 + (-2) = 1
Product of roots = 3 × (-2) = -6
Using x² - (sum of roots)x + (product of roots) = 0
Required equation: x² - x - 6 = 0 Shortcut Trick #3 - Vieta's Relations: Instead of finding individual roots, use sum and product formulas directly. This is especially useful when questions ask about expressions involving roots without finding the actual roots. Common Trap - The #1 Mistake: Students often forget to check if 'a' equals zero. If a = 0, the equation becomes linear (bx + c = 0), not quadratic. Always verify that the coefficient of x² is non-zero before applying quadratic methods. Another common error is sign mistakes while applying the quadratic formula, especially with the discriminant calculation. Exam Strategy: For SSC CGL, master middle term splitting first as it's faster than the quadratic formula. Practice identifying perfect squares quickly. Word problems often lead to quadratic equations, so focus on translation skills. Time management is crucial - spend maximum 2 minutes per quadratic equation question.