Advertisements
Advertisements
प्रश्न
Solve `|(4 - x, 4 + x, 4 + x),(4 + x, 4 - x, 4 + x),(4 + x, 4 + x, 4 - x)|` = 0
उत्तर
`|(4 - x, 4 + x, 4 + x),(4 + x, 4 - x, 4 + x),(4 + x, 4 + x, 4 - x)|` = 0
Put x = 0
`|(4 - 0, 4 + 0, 4 + 0),(4 + 0, 4 - 0, 4 + 0),(4 + 0, 4 + 0, 4 - 0)|` = 0
`|(4, 4, 4),(4, 4, 4),(4, 4, 4)|` = 0
0 = 0
∴ x = 0 satisfies the given equation.
Hence x = 0 is a root of the given equation.
Since three rows are identical, x = 0 is a root of multiplicity 2.
Since the degree of the product of the leading diagonal elements (4 – x)(4 – x)(4 – x) is 3.
There is one more root for the given equation.
`|(4 - x, 4 + x, 4 + x),(4 + x, 4 - x, 4 + x),(4 + x, 4 + x, 4 - x)|` = 0
`"C"_1 -> "C"_1 + "C"_2 + "C"_3`
`|(4 - x + 4 + x + 4 + x, 4 + x, 4 + x),(4 + x + 4 - x + 4 + x, 4 - x, 4 + x),(4 + x + 4 + x + 4 - x, 4 + x, 4 - x)|` = 0
`|(12 + x, 4 + x, 4 + x),(12 + x, 4 - x, 4 + x),(12 + x, 4 + x, 4 - x)|` = 0
Put x = – 12
`|(12 - 12, 4 - 12, 4 - 12),(12 - 12, 4 + 12, 4 - 12),(12 - 12, 4 - 12, 4 + 12)|` = 0
`|(0, -8, -8),(0, 16, -8),(0, -8, 16)|` = 0
0 = 0
∴ x = – 12 is a root of the given equation.
Hence, the required roots are x = 0, 0, – 12
APPEARS IN
संबंधित प्रश्न
If a, b, c are pth, qth and rth terms of an A.P, find the value of `|("a", "b", "c"),("p", "q", "r"),(1, 1, 1)|`
Show that `|("a"^2 + x^2, "ab", "ac"),("ab", "b"^2 + x^2, "bc"),("ac", "bc", "c"^2 + x^2)|` is divisiible by x4
Without expanding, evaluate the following determinants:
`|(2, 3, 4),(5, 6, 8),(6x, 9x, 12x)|`
Without expanding, evaluate the following determinants:
`|(x + y, y + z, z + x),(z, x, y),(1, 1, 1)|`
If A and B are square matrices of order 3 such that |A| = –1 and |B| = 3, find the value of |3AB|
If λ = – 2, determine the value of `|(0, lambda, 1),(lambda^2, 0, 3lambda^2 + 1),(-1, 6lambda - 1, 0)|`
Show that `|("b" + "c", "a" - "c", "a" - "b"),("b" - "c", "c" + "a", "b" - "a"),("c" - "b", "c" - "a", "a" + b")|` = 8abc
Show that `|(1, 1, 1),(x, y, z),(x^2, y^2, z^2)|` = (x – y)(y – z)(z – x)
Identify the singular and non-singular matrices:
`[(1, 2, 3),(4, 5, 6),(7, 8, 9)]`
Determine the values of a and b so that the following matrices are singular:
A = `[(7, 3),(-2, "a")]`
Choose the correct alternative:
The value of the determinant of A = `[(0, "a", -"b"),(-"a", 0, "c"),("b", -"c", 0)]` is
The remainder obtained when 1! + 2! + 3! + ......... + 10! is divided by 6 is,
If P1, P2, P3 are respectively the perpendiculars from the vertices of a triangle to the opposite sides, then `cosA/P_1 + cosB/P_2 + cosC/P_3` is equal to
A pole stands vertically inside a triangular park ΔABC. If the angle of elevation of the top of the pole from each corner of the park is same, then in ΔABC the foot of the pole is at the
What is the value of Δ if, Δ = `|(0, sin alpha, - cos alpha),(-sin alpha, 0, sin beta),(cos alpha, - sin beta, 0)|`
Choose the correct option:
Let `|(0, sin theta, 1),(-sintheta, 1, sin theta),(1, -sin theta, 1 - a)|` where 0 ≤ θ ≤ 2n, then
For f(x)= `ℓn|x + sqrt(x^2 + 1)|`, then the value of`g(x) = (cosx)^((cosecx - 1))` and `h(x) = (e^x - e^-x)/(e^x + e^-x)`, then the value of `|(f(0), f(e), g(π/6)),(f(-e), h(0), h(π)),(g((5π)/6), h(-π), f(f(f(0))))|` is ______.
`|("b" + "c", "c", "b"),("c", "c" + "a", "a"),("b", "a", "a" + "b")|` = ______.
If `x∈R|(8, 2, x),(2, x, 8),(x, 8, 2)|` = 0, then `|x/2|` is equal to ______.
If a, b, c, are non zero complex numbers satisfying a2 + b2 + c2 = 0 and `|(b^2 + c^2, ab, ac),(ab, c^2 + a^2, bc),(ac, bc, a^2 + b^2)|` = ka2b2c2, then k is equal to ______.
