CAT Quantitative Aptitude Questions | CAT Algebra - Linear Equations; Quadratic Equations

The question is about Real roots. Framing and solving equations is an integral part of Linear Equations and Quadratic Equations. Get as much practice as you can in these two topics because the benefits of being good at framing equations will be useful in other concepts. Note: If roots are real, then the discriminant is ≥ 0.

Question 16: If f(y) = x² + (2p + 1)x + p² - 1 and  x is a real number, for what values of ‘p' the function becomes 0?

1. p > 0
2. p > -1
3. p ≥ \\frac{-5}{4}\\)
4. p ≤ \\frac{3}{4}\\)

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Quadratic Equations: If roots are real then the discriminant is ≥ 0.

The function f(y) is a quadratic equation.
It is given that x is real.
So the discriminant of f(y) ≥ 0 
i.e. D = b² - 4ac ≥ 0 or
(2p + 1)² – 4(p² - 1) ≥ 0
4p² + 4p + 1 – 4 (p² - 1)  ≥ 0
4p + 5 ≥ 0
Or p ≥ \\frac{-5}{4}\\)

The question is "If f(y) = x² + (2p + 1)x + p² - 1 and  x is a real number, for what values of ‘p' the function becomes 0?"

Hence the answer is "p ≥ \\frac{-5}{4}\\)"

Choice C is the correct answer.