Question

find the factor polynomial given below.

$\frac{1}{2} {x}^{2} - 3x + 4$
​

Answer 1

$\mathfrak{\bf{\underline{\underline{Qᴜᴇsᴛɪᴏɴ \ ⇒}}}}$

$ㅤㅤㅤ ㅤㅤㅤ \frac{1}{2} {x}^{2} - 3x + 4 = 0$

$\mathfrak{\bf{\underline{\underline{Tᴏ \ Fɪɴᴅ \ ⇒}}}}$

ㅤㅤㅤ ㅤㅤㅤFᴀᴄᴛᴏʀ Oғ Pᴏʟʏɴᴏᴍɪᴀʟ

$\mathfrak{\bf{\underline{\underline{Sᴏʟᴜᴛɪᴏɴ \ ⇒}}}}$

➪ STEP 1 :- Rᴇᴀʀʀᴀɴɢɪɴɢ Tʜᴇ Eǫᴜᴀᴛɪᴏɴ.

ㅤㅤㅤㅤMᴜʟᴛɪᴘʟʏ Tʜᴇ Wʜᴏʟᴇ Eǫᴜᴀᴛɪᴏɴ Bʏ 2

$ㅤㅤㅤㅤㅤㅤ {x}^{2} - 6x + 8 = 0$

➪ STEP 2 :- FINDING FACTORS OF 8 WHOSE

ㅤㅤㅤㅤ ㅤSUM OR DIFFRENCE IS (-6).

$ㅤㅤㅤ ㅤㅤ {x}^{2} - 4x - 2x + 8 = 0 \\ ㅤㅤㅤㅤㅤ\underline {{x}^{2} - 4x} - \: \underline{2x + 8 }= 0$

➪ STEP 3 :- TAKING COMMON FROM TWO GROUPS

$ㅤㅤㅤ ㅤㅤx(x - 4) \: \: - 2(x - 4) = 0$

➪ STEP 4 :- EQUATING EACH EQUATION WITH R.H.S

ㅤㅤㅤ

$ㅤㅤㅤ ㅤx - 4 = 0 \: \: \: \: \: \: \:OR \: \: \: \: \: \: x - 2 = 0 \\ ㅤㅤㅤ ㅤx = 4 \: \: \: \: \: \: \: \: \: OR \: \: \: \: \: \: \: \: \: x = 2$

$</strong><strong>\</strong><strong>s</strong><strong>t</strong><strong>a</strong><strong>r</strong><strong>\mathfrak{\bf{\underline{\underline{Answer \ </strong><strong>⇒</strong><strong>}}}}$

$ㅤㅤㅤ ㅤㅤ\boxed {x = 4 }\: \: \: \: \: \: \:OR \: \: \: \: \: \: \: \boxed {x = 2}$