Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains 9 and -1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was

A) \( x^{2}\)+\( 10x\)+\( 9\)=\( 0\)
B) \( x^{2}\)-\( 10x\)+\( 16\)=\( 0\)
C) \( x^{2}\)-\( 10x\)+\( 9\)=\( 0\)
D) None of the above

Correct Answer:


B) \( x^{2}\)-\( 10x\)+\( 16\)=\( 0\)

Description for Correct answer:
The equation with roots -9 and -1 is , \( \Large (x+9)(x+1) = x^{2} + 10x +9 \) The equation with roots 8 and 2 is (x - 8)(x - 2) = \( \Large x^{2} - 10x + 16 \) The correct equation was \( \Large x^{2} - 10x + 16 \)

Hence option (B)is correct.

Part of solved CDS Maths(2) questions and answers : Exams >> CDSE >> CDS Maths(2)

Comments

Similar Questions

1). If m and n are the roots of the equation \( \large ax^{2}\)+\(bx \)+\( c\) =0 then the equation whose roots are \( \Large \frac{\left(m ^{2}+ 1\right)}{m} \) and \( \Large \frac{\left(n^{2}+1\right)}{n} \) is

A). \( acx^{2}\)+\( \left( ab+bc\right)\)\( x\)+\( b^{2}\)+\( \left( a-c\right)^{2}\)=\( 0\)

B). \( acx^{2}\)+\( \left( ab-bc\right)\)\( x\)+\( b^{2}\)+\( \left( a-c\right)^{2}\)=\( 0\)

C). \( acx^{2}\)+\( \left( ab-bc\right)\)\( x\)+\( b^{2}\)-\( \left( a-c\right)^{2}\)=\( 0\)

D). \( acx^{2}\)+\( \left( ab+bc\right)\)\( x\)+\( b^{2}\)-\( \left( a-c\right)^{2}\)=\( 0\)

2). The value of \( x^{2} - 4x + 11 \) can never be less than

A). 7

B). 8

C). 11

D). 22

3). If \( \Large \left( x^{2} + \frac{1}{x^{2}} \right) = \frac{17}{4}\), then what is \( \Large \left( x^{3} - \frac{1}{x^{3}} \right) \) equal to?

A). \( \Large \frac{75}{11} \)

B). \( \Large \frac{63}{8} \)

C). \( \Large \frac{95}{8} \)

D). None of these

4). \( 3x^{4}\)-\( 2x^{3}\)+\( 3x^{2}\)-\( 2x\)+\( 3\) divided by \( \left( 3x+2\right)\), then the remainder is

A). \( 0\)

B). \( \Large \frac{185}{27} \)

C). \( \Large \frac{181}{25} \)

D). \( \Large \frac{3}{4} \)

5). What should be added to the expression\(x \)\( \left( x+a\right)\)\( \left( x+2a\right)\)\( \left( x+3a\right)\) so that the sum may ba a perfect square?

A). \( 9a^{2}\)

B). \( 4a^{2}\)

C). \( a^{4}\)

D). None of these

6). If the roots of the equation \(Ax^{2} \)+\( Bx\)+\( C\) =0 are -1 and 1 then which one of the following is correct?

A). A andC are both zero

B). A and B are both positive

C). A and C are both negative

D). A and C are of opposite sign

7). If A and B are any two non-empty subsets of a set E. then what is \( A \cup ( A \cap B) \) equal to?

A). \( A\cap B \)

B). \( A\cup B \)

C). A

D). B

8). Consider the following in respect of the numbers \( \large \sqrt{2},\sqrt[3]{3},\sqrt[6]{6} \)
1. \( \large\sqrt[6]{6} \)is the greatest number.
2. \( \large\sqrt{2} \)is the smallest number.
Which of the above statements is/are correct?

A). 1 only

B). 2 only

C). Both 1 and 2

D). Neither 1 nor 2

9). A water pipe is cut into two pieces. The longer piece is 70% of the length of the pipe. By how much percentage is the longer piece longer than the shorter piece?

A). 140%

B). 400/3 %

C). 40 %

D). None of these

10). The sum of two positive numbers at and y is 2.5 times their difference. If the product of the numbers is 84, then what is the sum of the two numbers?

A). 26

B). 24

C). 22

D). 20