Question

Solve the following Quadratic Equation :

x² - 7x + 3 = 0​

Answer 1

Given : x² - 7x + 3 = 0

⠀⠀ ⠀

⠀⠀ ⠀ ★ Here,

⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀ † a = 1

⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀ † b = -7

⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀ † c = 3

⠀⠀ ⠀

Now, We Know The Formula :

⠀⠀

⠀⠀$\:\:\:\:\:\:\:{\blue{\bold{❍}}}\:{\underbrace{\red{\sf{x\:=\:{\dfrac{-b\:\pm\:\sqrt{b²\:-\:4ac}}{2a}}}}}}$

⠀⠀

$\:\dashrightarrow\:\small\sf{x\:=\:{\dfrac{-\:(-7)\:\pm\:\sqrt{(-7)²\:-\:4\:\times\:1\:\times\:3}}{2\:\times\:1}}}$

⠀⠀

$\:\:\:\:\:\:\:\:\:\:\dashrightarrow\:\sf{x\:=\:{\dfrac{7\:\pm\:\sqrt{49\:-\:12}}{2}}}$

⠀⠀

$\:\:\:\:\:\:\:\:\:\:\dashrightarrow\:\sf{x\:=\:{\dfrac{7\:\pm\:\sqrt{37}}{2}}}$

⠀⠀

$\:\:\:\:\:\:\:\:\:\:\dashrightarrow\:\sf{x\:=\:{\dfrac{7\:\pm\:6.08}{2}}}$

⠀⠀

☯ Taking positive sign,

⠀⠀

$\:\:\:\:\:\:\:\:\:\:\dashrightarrow\:\sf{x\:=\:{\dfrac{7\:+\:6.08}{2}}\:=\:{\pink{6.54}}}$

⠀⠀

☯ Taking negative sign,

⠀⠀

$\:\:\:\:\:\:\:\:\:\:\dashrightarrow\:\sf{x\:=\:{\dfrac{7\:-\:6.08}{2}}\:=\:{\pink{0.46}}}$

⠀

Hence,

$\:\:\:\:\:\:\:\therefore\:{\underline{\sf{The\:Quadratic \:Equation\:is\:{\textsf{\textbf{6.54}}}\:and\:{\textsf{\textbf{0.46}}}}}}.$

⠀

⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀⠀ ⠀${\textsf{\textbf{\purple{@IᴛᴢAᴀᴋʀɪᴛɪᥫ᭡}}}}$

Answer 2

Given : x² - 7x + 3 = 0

⠀⠀ ⠀

⠀⠀ ⠀ ★ Here,

⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀ † a = 1

⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀ † b = -7

⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀ † c = 3

⠀⠀ ⠀

Now, We Know The Formula :

⠀⠀

⠀⠀\:\:\:\:\:\:\:{\blue{\bold{❍}}}\:{\underbrace{\red{\sf{x\:=\:{\dfrac{-b\:\pm\:\sqrt{b²\:-\:4ac}}{2a}}}}}}❍

x=

2a

−b±

b²−4ac

⠀⠀

\:\dashrightarrow\:\small\sf{x\:=\:{\dfrac{-\:(-7)\:\pm\:\sqrt{(-7)²\:-\:4\:\times\:1\:\times\:3}}{2\:\times\:1}}}⇢x=

2×1

−(−7)±

(−7)²−4×1×3

⠀⠀

\:\:\:\:\:\:\:\:\:\:\dashrightarrow\:\sf{x\:=\:{\dfrac{7\:\pm\:\sqrt{49\:-\:12}}{2}}}⇢x=

2

7±

49−12

⠀⠀

\:\:\:\:\:\:\:\:\:\:\dashrightarrow\:\sf{x\:=\:{\dfrac{7\:\pm\:\sqrt{37}}{2}}}⇢x=

2

7±

37

⠀⠀

\:\:\:\:\:\:\:\:\:\:\dashrightarrow\:\sf{x\:=\:{\dfrac{7\:\pm\:6.08}{2}}}⇢x=

2

7±6.08

⠀⠀

☯ Taking positive sign,

⠀⠀

\:\:\:\:\:\:\:\:\:\:\dashrightarrow\:\sf{x\:=\:{\dfrac{7\:+\:6.08}{2}}\:=\:{\pink{6.54}}}⇢x=

2

7+6.08

=6.54

⠀⠀

☯ Taking negative sign,

⠀⠀

\:\:\:\:\:\:\:\:\:\:\dashrightarrow\:\sf{x\:=\:{\dfrac{7\:-\:6.08}{2}}\:=\:{\pink{0.46}}}⇢x=

2

7−6.08

=0.46

⠀

Hence,

\:\:\:\:\:\:\:\therefore\:{\underline{\sf{The\:Quadratic \:Equation\:is\:{\textsf{\textbf{6.54}}}\:and\:{\textsf{\textbf{0.46}}}}}}.∴

TheQuadraticEquationis6.54and0.46

.

⠀

⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀⠀ ⠀