Quadratic Equations CAT Problems

0
2957
Quadratic Equations CAT Problems
Quadratic Equations Problems for CAT

Quadratic equations CAT problems consists of important quadratic equations questions for CAT. This CAT questions will be very useful for quantitative aptitude for CAT.

Taking a free CAT mock test and solving CAT past papers will definitely help you to get good understanding of the simple, linear and quadratic equations CAT questions.

You can download the Quadratic Equations CAT Problems or you can go through the details below.

Download Quadratic Equations CAT Problems PDF

6 Months Intensive Course @ Just Rs. 7999

Quadratic Equations CAT Problems:

Question 1:

Given the quadratic equation $x^2 – (A – 3)x – (A – 2)$, for what value of $A$ will the sum of the squares of the roots be zero?

A. -2

B. 3

C. 6

D. None of these

Question 2:

The roots of the equation $ax^{2} + 3x + 6 = 0$ will be reciprocal to each other if the value of a is

A. 3

B. 4

C. 5

D. 6

Question 3:

A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f (x) at x = 10?

A. -119

B. -159

C. -110

D. -180

Question 4:

If the roots of the equation $x^3 – ax^2 + bx – c = 0$ are three consecutive integers, then what is the smallest possible value of b?

A. $\frac{-1}{\sqrt 3}$

B. -1

C. 0

D. 1

Question 5:

If $xy + yz + zx = 0$, then $(x + y + z)^2$ equals

A. $(x + y)^2 + xz$

B. $(x + z)^2 + xy$

C. $x^2 + y^2 + z^2$

D. $2(xy + yz + xz)$

Download CAT Quantitative Aptitude Questions PDF

Take a free mock test for CAT

Solutions:

1) Answer (D)

For summation of square of roots to be zero, individual roots should be zero. Hence summation should be zero i.e.  A-3=0 ; A = 3 And product of roots will also be zero i.e. A-2 = 0 ; A =2 So there is no unique value of A which can satisfy above equation.

2) Answer (D)

If roots of given equation are reciprocal to each other than product of roots should be equal to 1.
i.e. $\frac{6}{a} = 1$
hence a=6

3) Answer (B)

Let the function be $ax^2 + bx + c$.
We know that x=0 value is 1 so c=1.
So equation is $ax^2 + bx + 1$.
Now max value is 3 at x = 1.
So after substituting we get a + b = 2.
If f(x) attains a maximum at ‘a’ then the differential of f(x) at x=a, that is, f'(a)=0.
So in this question f'(1)=0
=> 2*(1)*a+b = 0
=> 2a+b = 0.
Solving the equations we get a=-2 and b=4.
$ -2x^2 + 4x + 1$ is the equation and on substituting x=10, we get -159.

4) Answer (B)

b = sum of the roots taken 2 at a time.
Let the roots be n-1, n and n+1.
Therefore, $b = (n-1)n + n(n+1) + (n+1)(n-1) = n^2 – n + n^2 + n + n^2 – 1$
$b = 3n^2 – 1$. The smallest value is -1.

5) Answer (C)

$(x+y+z)^2 = x^2 + y^2 + z^2 + 2(xy + yz + xz)$
as $xy+yz+xz = 0$
so equation will be resolved to $x^2 + y^2 + z^2$

Hope you will find this quadratic equations CAT Problems useful, you can also download all our CAT Verbal Ability PDF’s.

CAT Previous Solved Papers

 

LEAVE A REPLY

Please enter your comment!
Please enter your name here