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

Question

If f(x)=| x -3 2 x2-18 3 x3-81 x -5 2 x2-50 4 x3-500 1 2 3| 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

f(x)=(x-3)(x-5)|1 2(x+3) 3(x2+9+3 x) 1 2(x+5) 4(x2+25+5 x) 1 2 3| ⇒ f(3)=f(5)=0 So, f(1) f(3)+f(3) ⋅ f(5)+f(5) f(1)=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

$f (1)$

$f (3)$

$f (1) + f (3)$

$f (1) + f (5)$

$f (x) = (x - 3) (x - 5) ∣ ∣ 111 2 (x + 3) 2 (x + 5) 2 3 (x^{2} + 9 + 3 x) 4 (x^{2} + 25 + 5 x) 3 ∣ ∣$
$\Rightarrow f (3) = f (5) = 0$
So, $f (1) f (3) + f (3) \cdot f (5) + f (5) f (1) = 0 = f (3)$

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)