DeterminantHard
Question
Let ᐃ = 
, then
, then Options
A.1 - x3 is a factor of ᐃ
B.(1 - x3)2 is factor of ᐃ
C.ᐃ(x) = 0 has 4 real roots
D.ᐃ′(1) = 0
Solution
ᐃ = 
, ᐃ = (1 + x + x2) 
= (1 + x + x2) {1(1 - x3) - x(1 - x) + x2(x2 - 1)}
= (1 + x + x2) {1 - x3 - x + x2 + x4 - x2)
= (1 + x + x2) {x4 - x3 - x + 1)
ᐃ = (1 - x3)2
ᐃ′= 2(1 - x3) (-3 x2)
ᐃ′(1) = 0
, ᐃ = (1 + x + x2) = (1 + x + x2) {1(1 - x3) - x(1 - x) + x2(x2 - 1)}
= (1 + x + x2) {1 - x3 - x + x2 + x4 - x2)
= (1 + x + x2) {x4 - x3 - x + 1)
ᐃ = (1 - x3)2
ᐃ′= 2(1 - x3) (-3 x2)
ᐃ′(1) = 0
Create a free account to view solution
View Solution FreeMore Determinant Questions
Let M be a 3 × 3 non-singular matrix with det(M) = α. If M-1 adj(adj M) = kI, then the value of ′k′...The value of k for which the set of equations 3x + ky − 2z = 0, x + ky + 3z = 0 and 2x + 3y − 4z = 0 has a n...Let A and B be two 2 × 2 matrix with real entries. If AB = O and tr(A) = tr(B) = 0 then...If f′(x) =, then y = f(x) represents -...If a, b, c are all different and = 0, then:...