Question

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

Answer 1

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

__________________

Answer 2

Answer:

$\huge \tt \to\red {\frac{201}{64} }$

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,

$\to \tt f(1) = 5 ({1})^{4} - 3 ({1})^{3} + 2( {1})^{2} - 1 \\ \\ \tt \to f(1) = 5 \times 1 - 3 \times 1 + 2 \times 1 - 1 \\ \\ \tt \to f(1) = 5 - 3 + 2 - 1 \\ \\ \tt = 3$

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

$\tt \to f( - 1) = 5( { - 1})^{4} - 3 ({ - 1})^{3} + 2 ({ - 1})^{2} - 1 \\ \\ \tt \to f( - 1) = 5 \times 1 - 3 \times ( - 1) + 2 \times 1 - 1 \\ \\ \tt \to f( - 1) = 5 + 3 + 2 - 1 \\ \\ \tt = 9$

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

$\tt \to f(2) = 5( {2})^{4} - 3 ({2})^{3} + 2( {2})^{2} - 1 \\ \\ \tt \to f(2) = 5 \times 16 - 3 \times 8 + 2 \times 2 - 1 \\ \\ \tt \to f(2) = 80 - 24 + 4 - 1 \\ \\ \tt = 64$

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

$\tt \huge \to3 + \frac{9}{64} = \frac{64 \times 3 + 9}{64} \\ \\ \tt \huge = \frac{201}{64}$

☞︎︎︎ Tʜᴀɴᴋs ғᴏʀ ǫᴜᴇsᴛɪᴏɴ