5 CAT Quadratic Equations Problems (with solutions) you should solve

Introduction:

Quadratic Equations is an important topic in CAT Algebra. The best way to master a topic is to practice problems and we bring to you this set of 5 quadratic equation problems that you can use for the same.

Question 1: Let a, b, c be real numbers a≠0. If p is a root of a²y²+by + c = 0, q is the root of a²y²+by + c = 0 and 0 <p< q, then the equation a²y²+by + c = 0 has a root r that always satisfies

(a) r = (p+q)/2
(b) r = p + (q/2)
(c) r = a
(d) p <r <q

Question 2: Let p, q be the roots of the equation (x-a)(x-b) = c, c is not equal to 0 . Then the roots of the equation (x-p)(x-q) + c = 0 are
(a) a, c
(b) b, c
(c) a, b
(d) a + c, b + c

Question 3: If the roots of the equation x²-2bx+b²+b-3 = 0  are real and less than 3, then
(a) – 4 <b< 2
(b) 2<b< 3
(c) 0 <b< 4
(d) b> 3

Question 4:

If p and q (p<q) are the roots of the equation x²+bx+c = 0 ,  where c< 0 <b.
(a) 0<p<q
(b) p< 0 <q< |p|
(c) p < q< 0
(d) p < 0 |p| <q

Question 5: For all ‘x’, x²+2px+(10 – 3p)>0, then the interval in which ‘p’ lies is
(a) p< –5
(b) –5 <p < 2
(c) p > 5
(d) 2 <p< 5

Extra tips for CAT Quadratic Equations
• Quadratic equation is a top that massively features in class 11 and class 12 mathematics. In order to learn the absolute basics of the topic, it is recommended that you take up some basic level books from these classes.
• You can use class 11 NCERT or RD Sharma book to learn the basics of the topic.
• Make sure you also learn the graphical approach for these questions as this will help you master problems for this topic.