Quadratic Equations Problems : CAT 2016 Quant / Math Prep
Question 4 the day : March 12, 2003
The question for the day is from the topic Quadratic Equations. The question is about finding the value of an expression after evaluating the roots of a quadratic equation.
Question
If p and q are the roots of the equation x^{2}  bx + c = 0, then what is the equation if the roots are (pq + p + q) and (pq  p  q)?
(1) x^{2}  2cx + (c^{2}  b^{2}) = 0
(2) x^{2 } 2bx + (b^{2} + c^{2}) = 0
(3) Bcx^{2}  2(b+c)x + c^{2} = 0
(4) x^{2} + 2bx  (c^{2}  b^{2}) = 0
Correct Choice is (1). Correct Answer is x^{2}  2cx + (c^{2}  b^{2}) = 0
Explanatory Answer
In the given quadratic equation x^{2}  bx + c = 0,
The sum of the roots p + q = b  (1)
And the product of the roots pq = c  (2)
We have to formulate a quadratic equation whose roots are (pq + p + q) and (pq  p  q).
The sum of the two roots = pq + p +q + pq  p  q = 2pq
But from eqn (2), we know that pq = c
Therefore, the sum of the roots = 2c
The product of the roots = (pq + p + q)(pq  p  q)= (pq)^{2}  (p+q)^{2}
From equation (1) and (2), we know that pq = c and p + q = b
Therefore, the product of the roots = c^{2}  b^{2}
We know the sum of the roots and the product of the roots.
Therefore, the quadratic equation is x^{2}  (sum of
the roots)x + product of the roots = 0
=> x^{2}  2cx + c^{2}  b^{2} = 0
More Questions on Linear, Quadratic and Cubic Equations  Algebra
XLRI XAT TANCET Practice Question Samples
Sorted by Subject
Algebra,
Arithmetic & Geometric Progressions,
Averages and Mean,
Clocks and Calendars,
Data Sufficiency,
English Grammar,
Function,
Geometry,
Coordinate Geometry,
Mensuration,
Trigonometry,
Interest,
Inequality,
Mixtures & Alligations,
Number System and Theory,
Percentages,
Profit & Loss,
Permutation & Combination,
Probability,
Ratio, Proportion,
Set Language and Theory,
Speed, Time & Distance,
Races,
Pipes & Cisterns And Work & Time,
Miscellaneous,
General Knowledge.


Quick Links
TANCET Questionbank 

TANCET MBA MCA Practice Questions with detailed explanation and shortcuts.


GMAT Math Books 

Comprehensive study material for GMAT Quant. 1800+ questions.


Staying outside India? 

Ascent offers CAT Correspondence Course for those who reside abroad.


CAT classes @ Chennai 

CAT 2010 intensive batch starts Jan 23, 10. Faculty includes IIM graduates. Personal attention. Online Mock CATs & Analysis.


