if the polynomial is given by f(x)= 5x⁴-3x³+2x²-1, find f(1)+f(-1)/f(2)​

2 thoughts on “if the polynomial is given by f(x)= 5x⁴-3x³+2x²-1, find f(1)+f(-1)/f(2)​”

1. Answer:

   [tex] \huge \tt \to\red {\frac{201}{64} }[/tex]

   Step-by-step explanation:

   Gɪᴠᴇɴ ᴘᴏʟʏɴᴏᴍɪᴀʟ :-

   • f(x)= 5x⁴-3x³+2x²-1,

   Tᴏ ғɪɴᴅ :-

   •f(1)+f(-1)/f(2)

   ❀Wᴇ ʜᴀᴠᴇ ᴛᴏ ᴘᴜᴛ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏɴᴇ ʙʏ ᴏɴᴇ.

   ☞︎︎︎Fɪʀsᴛ ᴋᴇᴇᴘ f(1) in f(x)= 5x⁴-3x³+2x²-1,

   [tex] \to \tt f(1) = 5 ({1})^{4} – 3 ({1})^{3} + 2( {1})^{2} – 1 \\ \\ \tt \to f(1) = 5 \times 1 – 3 \times 1 + 2 \times 1 – 1 \\ \\ \tt \to f(1) = 5 – 3 + 2 – 1 \\ \\ \tt = 3[/tex]

   ☞︎︎︎ Nᴏᴡ ᴋᴇᴇᴘ f(-1) in f(x)= 5x⁴-3x³+2x²-1,

   [tex] \tt \to f( – 1) = 5( { – 1})^{4} – 3 ({ – 1})^{3} + 2 ({ – 1})^{2} – 1 \\ \\ \tt \to f( – 1) = 5 \times 1 – 3 \times ( – 1) + 2 \times 1 – 1 \\ \\ \tt \to f( – 1) = 5 + 3 + 2 – 1 \\ \\ \tt = 9[/tex]

   ☞︎︎︎Nᴏᴡ ᴋᴇᴇᴘ f(2) in f(x)= 5x⁴-3x³+2x²-1,

   [tex] \tt \to f(2) = 5( {2})^{4} – 3 ({2})^{3} + 2( {2})^{2} – 1 \\ \\ \tt \to f(2) = 5 \times 16 – 3 \times 8 + 2 \times 2 – 1 \\ \\ \tt \to f(2) = 80 – 24 + 4 – 1 \\ \\ \tt = 64[/tex]

   ❥︎Nᴏᴡ ғɪɴᴅ f(1)+f(-1)/f(2) ʙʏ ᴋᴇᴇᴘ ᴛʜᴇɪʀ sᴜɪᴛᴀʙʟᴇ ᴠᴀʟᴜᴇs,

   [tex] \tt \huge \to3 + \frac{9}{64} = \frac{64 \times 3 + 9}{64} \\ \\ \tt \huge = \frac{201}{64} [/tex]

   ☞︎︎︎ Tʜᴀɴᴋs ғᴏʀ ǫᴜᴇsᴛɪᴏɴ

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2. Solution

   Given :–

   • polynomial equation, f(x) = 5x⁴ – 3x³ + 2x² – 1

   Find :–

   • Value of f(1) + f(-1)/f(2)

   Explanation

   First Calculate, f(1).

   Keep x = 1 in this Equation

   ==> f(1) = 5×(1)⁴ – 3×(1)³ + 2×(1)² – 1

   ==> f(1) = 5 – 3 + 2 – 1

   ==> f(1) = 7 – 4.

   ==> f(1) = 3 .

   Now, Calculate f(–1)

   keep x = –1 .

   ==> f(-1) = 5×(-1)⁴ – 3(-1)³ + 2(-1)² – 1

   ==> f(-1) = 5 + 3 +2 – 1

   ==> f(-1) = 10 – 1.

   ==> f(-1) = 9.

   Now, Calculate f(2)

   ==> f(2) = 5(2)⁴ -3(2)³ + 2(2)² – 1

   ==> f(2) = 80 – 24 + 8 – 1

   ==> f(2) = 88 – 25

   ==> f(2) = 64 .

   Now, keep all above Values in f(1) + f(–1)/f(2)

   = 3 + 9/64

   = (3×64+9)/64

   = (192+9)/64

   = 201/64

   Hence

   • Value of f(1) + f(-1)/f(2) will be = 201/64

   __________________

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