Linear, quadratic, cubic equations, roots of equations. Algebra IIM CAT, XAT Quant sample Questions : CAT, MBA Entrance Test Questions

Question 4 the day : March 2, 2004
The question for the day is a sample practice problem in quadratic equation. Helps understand concepts related to roots of a quadratic equation and the nature of the roots of the quadratic equation. The question for the day is on finding a missing co-efficient from the topic quadratic equation..

Question
If one of the roots of the quadratic equation x² + mx + 24 = 0 is 1.5, then what is the value of m?

1. -22.5
2. 16
3. -10.5
4. -17.5

Correct Answer is -17.5. Correct Choice is (4)

Explanatory Answer

We know that the product of the roots of a quadratic equation ax² + bx + c = 0 is

In the given equation, x² + mx + 24 = 0, the product of the roots = = 24.
The question states that one of the roots of this equation = 1.5.
If x₁ and x₂ are the roots of the given quadratic equation and let x₁ = 1.5.
Therefore, x₂ == 16.
In the given equation, m is the co-efficient of the x term.
We know that the sum of the roots of the quadratic equation ax² + bx + c = 0 is = -m
Sum of the roots = 16 + 1. 5 = 17 = -17.5.
Therefore, the value of m = -17.5

Sorted by Subject
Algebra, Arithmetic & Geometric Progressions, Averages and Mean, Clocks and Calendars, Data Sufficiency, English Grammar, Function, Geometry, Interest, Inequality, Mensuration, Mixtures & Alligations, Number System and Theory, Percentages, Permutation & Combination, Pipes & Cisterns And Work & Time, Probability, Profit & Loss, Races, Ratio, Proportion, Set Language and Theory, Speed, Time & Distance, Trigonometry, Miscellaneous, General Knowledge.

Sorted by Date

2003
January 2003, February 2003, March 2003, April 2003, May 2003, June 2003, July 2003, August 2003, September 2003, October 2003, November 2003.

2004
February 2004, March 2004, April 2004, May 2004, June 2004, July 2004, August 2004, November 2004, December 2004.