Algebra - Quadratic Equations - Previous Year CAT/MBA Questions
The best way to prepare for Algebra - Quadratic Equations is by going through the previous year Algebra - Quadratic Equations CAT questions. Here we bring you all previous year Algebra - Quadratic Equations CAT questions along with detailed solutions.
Click here for previous year questions of other topics.
It would be best if you clear your concepts before you practice previous year Algebra - Quadratic Equations CAT questions.
Join our Telegram Group for CAT/MBA Preparation.
If the roots x1 and x2 of the quadratic equation x2 − 2x + c = 0 also satisfy the equation 7x2 – 4x1 = 47, then which of the following is true?
- (a)
c = -15
- (b)
x1 = -5, x2 = 3
- (c)
x1 = 4.5, x2 = -2.5
- (d)
None of these
Answer: Option A
Join our Telegram Group for CAT/MBA Preparation.
Text Explanation :
We know that the sum of the roots = .
Hence, x1 + x2 = 2. Now we have two equations, viz. x1 + x2 = 2 ...(i)
and 7x2 – 4x1 = 47 ...(ii)
Solving these two equations, we get x1 = –3 and x2 = 5. Since it does not satisfy options (b) and (c), we will verify it for option (a).
The product of the roots = (–3) × 5 = –15, in our case is c. Hence, c = –15.
Alternately,
Put values of x1, x2 in equation (ii). Do not match. So put c = –15 in equation (i) to get the roots of equation. After finding the roots of equation (i), check whether they satisfy equation (ii) or not.
The roots (5, –3) satisfy the equation (ii) so answer is (a).
Hence, option (a).
Workspace:
Given the quadratic equation x2 – (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
Answer: Option D
Join our Telegram Group for CAT/MBA Preparation.
Text Explanation :
If we write the given equation in the conventional form, i.e. ax2 + bx + c, a = 1, b = – (A – 3), i.e. (3 – A) and c = –(A – 2), i.e. (2 – A).
Let the roots of this equation be α and β. So the sum of the squares of the roots = α2 + β2 = (α + β)2 – 2αβ.
Now (α + β) = Sum of the roots =
and αβ = Product of the roots = (2 - A).
Hence, α2 + β2 = (A – 3)2 – 2(2 – A) = A2 – 4A + 5 = 0.
Discriminant of this equation is less than 0, hence there no real value of A possible.
Hence, option (d).
Workspace:
One root of x2 + kx – 8 = 0 is square of the other. Then the value of k is
- (a)
2
- (b)
8
- (c)
-8
- (d)
-2
Answer: Option D
Join our Telegram Group for CAT/MBA Preparation.
Text Explanation :
If the roots are a and a2, the product of roots = a3 = –8.
∴ a = –2.
Hence, sum of the roots = -k = (a + a2) = (–2 + 4) = 2.
∴ k = -2.
Hence, option (d).
Workspace:
Two positive integers differ by 4 and sum of their reciprocals is . Then one of the numbers is
- (a)
3
- (b)
1
- (c)
5
- (d)
21
Answer: Option A
Join our Telegram Group for CAT/MBA Preparation.
Text Explanation :
Let one of the numbers be x. So the other number would be (x + 4).
According to the question, we have 21 or x = 3.
Hint:
Please note that the sum of reciprocals is basically .
So we have to find two integers whose sum is 10 and whose product is 21.
So x + (x + 4) = 10 or x = 3.
Hence, option (a).
Workspace:
If one root of x2 − px + 12 = 0 is 4, while the equation x2 − px + q = 0 has equal roots, then the value of q is
- (a)
- (b)
- (c)
4
- (d)
Answer: Option A
Join our Telegram Group for CAT/MBA Preparation.
Text Explanation :
If one root of x2 + px + 12 = 0 is 4, then 42 + 4p + 12 = 0, i.e. p = –7.
x2 – px + q = 0 has equal roots.
If the roots are α each, 2α = - = 7, i.e., α = , and q = α2
Hence, option (a).
Workspace:
Feedback
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.