If f(x)=| beginmatrix x-3 2x2-18 3x3-81 x-5 2x2-50 4x3-500 1 2 3 endmatrix |, then f(1).f(3)+f(3).f(5)+f(5).f(1) is equal to:

Question

If f(x)=| beginmatrix x-3 2x2-18 3x3-81 x-5 2x2-50 4x3-500 1 2 3 endmatrix |, then f(1).f(3)+f(3).f(5)+f(5).f(1) is equal to: (A)  f(1)  (B)  f(3)  (C)  f(1)+f(3)  (D)  f(1)+f(5)

Tardigrade Admin · Accepted Answer

Q. If $f (x) = ∣ ∣ x - 3 x - 5 1 2 x^{2} - 18 2 x^{2} - 50 2 3 x^{3} - 81 4 x^{3} - 500 3 ∣ ∣,$ then $f (1) . f (3) + f (3) . f (5) + f (5) . f (1)$ is equal to:

$f (1)$

$f (3)$

$f (1) + f (3)$

$f (1) + f (5)$

$f (1) + f (3) + f (5)$

$∵$ $f (1) = ∣ ∣ - 2 - 4 1 - 16 - 48 2 - 78 4963 ∣ ∣$
$f (3) = ∣ ∣ 0 - 2 1 0 - 32 2 0 - 392 3 ∣ ∣ = 0$
and $f (5) = ∣ ∣ 201320229403 ∣ ∣ = 0$
$∴$ $f (1) . f (3) + f (3) - f (5) + f (5) . f (1)$
$= f (1) .0 + 0 + f (1) .0$ $= 0 = f (3)$

Q. If f(x)=∣∣​x−3x−51​2x2−182x2−502​3x3−814x3−5003​∣∣​, then f(1).f(3)+f(3).f(5)+f(5).f(1) is equal to:

f(1)

f(3)

f(1)+f(3)

f(1)+f(5)

f(1)+f(3)+f(5)

∵ f(1)=∣∣​−2−41​−16−482​−784963​∣∣​ f(3)=∣∣​0−21​0−322​0−3923​∣∣​=0 and f(5)=∣∣​201​3202​29403​∣∣​=0 ∴ f(1).f(3)+f(3)−f(5)+f(5).f(1) =f(1).0+0+f(1).0 =0=f(3)

Q. If $f (x) = ∣ ∣ x - 3 x - 5 1 2 x^{2} - 18 2 x^{2} - 50 2 3 x^{3} - 81 4 x^{3} - 500 3 ∣ ∣,$ then $f (1) . f (3) + f (3) . f (5) + f (5) . f (1)$ is equal to:

$f (1)$

$f (3)$

$f (1) + f (3)$

$f (1) + f (5)$

$f (1) + f (3) + f (5)$

$∵$ $f (1) = ∣ ∣ - 2 - 4 1 - 16 - 48 2 - 78 4963 ∣ ∣$
$f (3) = ∣ ∣ 0 - 2 1 0 - 32 2 0 - 392 3 ∣ ∣ = 0$
and $f (5) = ∣ ∣ 201320229403 ∣ ∣ = 0$
$∴$ $f (1) . f (3) + f (3) - f (5) + f (5) . f (1)$
$= f (1) .0 + 0 + f (1) .0$ $= 0 = f (3)$