Home
Class 12
MATHS
Using properties of determinant, If f(x)...

Using properties of determinant, If `f(x)= a + bx + cx^(2)`, prove that `|(a,b,c),(b,c,a),(c,a,b)|= -f(1)f(omega)f(omega^(2)), omega` is a cube root of unity

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MODEL TEST PAPER-5

    ICSE|Exercise Section-B|10 Videos

  • MODEL TEST PAPER-5

    ICSE|Exercise Section -C|10 Videos

  • MODEL TEST PAPER-16

    ICSE|Exercise SECTION -C (65 MARKS)|10 Videos

  • MODEL TEST PAPER-6

    ICSE|Exercise Section -C|10 Videos

Similar Questions

Explore conceptually related problems

If omega is a cube root of unity, then 1+omega = …..

If a , b , c are real numbers, prove that |[a,b,c],[b,c,a],[c,a,b]|=-(a+b+c)(c+b w+c w^2)(a+b w^2+c w), where w is a complex cube root of unity.

If omega is a cube root of unity, then 1+ omega^(2)= …..

Evaluate |(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega, omega)| where omega is cube root of unity.

Prove that the value of determinant |{:(1,,omega,,omega^(2)),(omega ,,omega^(2),,1),( omega^(2),, 1,,omega):}|=0 where omega is complex cube root of unity .

If omega is a cube root of unity, then omega + omega^(2)= …..

If f(x) = a + bx + cx^2 where a, b, c in R then int_o ^1 f(x)dx

If 1,omega,omega^2 are the cube roots of unity, then /_\ is equal to.....

If 1, omega and omega^(2) are the cube roots of unity, prove that (a+b omega+c omega^(2))/(c+a omega+b omega^(2))=omega^(2)

If omega is an imaginary cube root of unity, then the value of |(a,b omega^(2),a omega),(b omega,c,b omega^(2)),(c omega^(2),a omega,c)| , is

Home
Profile