Question

If f(x) = x4 -4x3 +3x2 -2x+1, then find whether f(0) X f(-1)=f(2)
i am giving 100 points and brainliest answer on correct answer​

Answer 1

$\red{ \qquad \underline{ \pmb{{ \mathbb{ \maltese  \:  COMPLETE \: \: QUESTION \:   \maltese }}}}}$

• If f(x) = x4 -4x3 +3x2 -2x+1, then find whether f(0) X f(-1)=f(2)

$\Large\green{\qquad\underline{\pmb{{ \mathbb { \maltese  \:  GIVEN \:  \maltese }}}}}$

${F(x) = x⁴ - 4x³ + 3x² - 2x +1}$

$\Large \orange{\qquad \underline{ \pmb{{ \mathbb{ \maltese  \:SOLUTION \:  \maltese }}}}}$

$f(0) × f(-1) = f(2)$

$♦ f(0) :-$

${f(0) = 0⁴ - 4×0³ + 3(0)² - 2(0) + 1}$

$f(0) = 0 - 0 + 0 - 0 + 1$

$f(0) = 1$

$♦ f(-1) :-$

${f(-1) = (-1)⁴ - 4(-1)³ + 3(-1)² - 2(-1) + 1}$

${f(-1) = 1 - (-4) + 3 -(-2) + 1}$

$f(-1) = 1 + 4 + 3+ 2 + 1$

$f(-1) = 11$

$♦ f(0) × f(-1) :-$

${f(0) × f(-1) = 1 × 11 = 11 ..eq(1)}$

$♦ f(2) :-$

${f(2) = (2)⁴ - 4(2)³ + 3(2)² - 2(2) + 1}$

$f(2) = 16 - 32 + 12 - 4 + 1$

$f(2) = - 16 + 9$

$f(2) = -7$

$\purple{\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese  \:  REQUIRED \: \: INFO \:  \maltese }}}}}$

$f(0) × f(-1) ≠ f(2)$

$\large \mathfrak{ \text{W}e \: \text{K}now }$

$Because ,$

$11 ≠ -7$

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$\huge\boxed{\dag\sf\red{Thanks}\dag}$