TCS NQT Guide TCS NQT Numerical AbilityLinear and Quadratic Equations Solution Tricks

Linear and Quadratic Equations Solution Tricks

Learn core concepts, essential formulas, and attempt practice questions designed on the latest TCS NQT testing patterns.

Key Concepts & Formulas

1Linear Eq: ax + b = 0 => x = -b/a.
2Quadratic Eq: ax^2 + bx + c = 0.
3Roots formula: x = [-b ± sqrt(b^2 - 4ac)] / 2a.
4Discriminant (D) = b^2 - 4ac. Real & Equal if D=0; Real & Unique if D>0; Complex if D<0.
5Sum of roots = -b/a. Product of roots = c/a.

Practice Question 1

Find the roots of the equation x^2 - 5x + 6 = 0.

A) 2, 3

B) 1, 6

C) -2, -3

D) -1, -6

Correct Answer: A) 2, 3

Step-by-step Solution: Factorizing x^2 - 5x + 6 = 0 => (x-2)(x-3) = 0 => x = 2 or x = 3.

Practice Question 2

What is the product of the roots of 3x^2 - 9x + 5 = 0?

A) 5/3

B) 3

C) -3

D) -5/3

Correct Answer: A) 5/3

Step-by-step Solution: Product of roots = c/a. In this equation, c = 5 and a = 3. Thus, the product is 5/3.

Solve quadratics using root sum (-b/a) and product (c/a) checks before resorting to the discriminant formula.