Question

Find the number of values of  t for which the system of equations

              

              

              

has non-trivial solution.

Solution

Correct option is

3

The given system of equations will have a non-trivial solution if

Clearly ∆ is a cubic polynomial in t and has 3 roots.

SIMILAR QUESTIONS

Q1

The complex number

                    

Q2

If a, b > 0 and

                    

then ∆ has a local minimum at x equal

Q3

If x, y, z are different from zero and

Q4

If p + q + r = a + b + c = 0, then the determinant

                 

Q5
Q6

      

Q7

If the system of the linear equations x + y + z = 6, x + 2y + 3z = 14 and 2 x + 5y + λz = μ, (λ, μ ∈ R)  has a unique solution, then

Q8
Q9

 

find the maximum value of f (x).

Q10

Find the number of real roots of the equation