1800-150-456-789
FlagBACK
Flag Algebra> Let a and b be the roots of equation Ax^2...
question mark

Let a and b be the roots of equation Ax^2+Bx+C=0.Evaluate the value of determinant | 31+a+b1+a^2 +b^2|| 1+a+b.1+a^2+b^21+a^3+b^3|| 1+a^2+b^2.1+a^3+b^3.1+a^4+b^4.|

bhumika gupta , 8 Years ago
Grade 12
anser 1 Answers
mycroft holmes

Last Activity: 8 Years ago

The given determinant can be written as a product:
\begin{vmatrix} 1 & 1 &1 \\ 1 & a& b\\ 1& a^2& b^2 \end{vmatrix} \ \times \begin{vmatrix} 1 & 1 &1 \\ 1 & a& b\\ 1& a^2 & b^2 \end{vmatrix}
 
= \begin{vmatrix} 1 & 1 &1 \\ 1 & a& b\\ 1& a^2& b^2 \end{vmatrix} ^2
 
Using the well known expansion for the Vandermonde Determinant, we can evaluate this as (a-b)^2 (a-1)^2(b-1)^2
 
Since a,b are roots of the quadratic Ax2+Bx+C, we have
 
(a-b)^2 = \frac{B^2-4AC}{A^2}
 
and (a-1)^2 (b-1)^2 = [(a-1)(b-1)]^2 = P(1)^2 = (A+B+C)^2
 
Hence given expressions equals
 
\frac{(B^2-4AC)(A+B+C)^2}{A^2}

Provide a better Answer & Earn Cool Goodies

Enter text here...
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Enter text here...

Other Related Questions on algebra

question mark
What is a binomial expression?
algebra
1 Answer Available

Last Activity: 1 Year ago

question mark
Can we divide two vectors? If this is possible then how?
algebra
1 Answer Available

Last Activity: 1 Year ago

question mark
How do you write “the product of 18 and q” as an algebraic expression?
algebra
1 Answer Available

Last Activity: 1 Year ago

question mark
दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे
algebra
0 Answer Available

Last Activity: 2 Years ago

question mark
Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?
algebra
1 Answer Available

Last Activity: 2 Years ago