Question

Solve the equation by quadratic formula method : x² + 9x - 3 = 0​

Answer 1

Given :-

• x² + 9x - 3 = 0

Solution :-

• a = 1
• b = 9
• c = - 3

Apply quadratic formula

→ D = b² - 4ac

where D is discriminant

→ D = (9)² - 4 × 1 × (-3)

→ D = 81 + 12

→ D = 93

Now,

→ x = - b ± √D/2a

So,

→ x = - b + √D/2a

→ x = -9 + √93/2 × 1

→ x = - 9 + √93/2

________________________________

→ x = - b - √D/2a

→ x = -9 - √93/2 × 1

→ x = - 9 - √93/2

Hence,

• x = - 9 + √93/2 or - 9 - √93/2

Answer 2

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$\: \: \huge\underline{\boxed { \bf{answer \ddot \frown}}}$

$\: \: \diamondsuit \bf{ {x}^{2} + 9x - 3 = 0} \: \: \: ......given \: quadratic \: equation$

$\: \: \\ \: \implies \underline{ \displaystyle \sf{ \: by \: using \: \: determinant \: form}}$

$\: \: \mapsto \sf{ { b}^{2} - 4ac}$

$\: \mapsto \sf{ {(9)}^{2} - 4(1)( - 3)}$

$\: \: \mapsto \sf{81 + 12}$

$\: \: \mapsto \sf{93}$

$\: \: \bigstar\underline{ \bf{ \: by \: using \: formula \: method}}$

$\: \: \implies \displaystyle \sf{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }$

$\: \: \implies \displaystyle \sf{x = \frac{ - 9 \pm \sqrt{93} }{2} }$

$\: \\ \implies \displaystyle \sf{x = \frac{ - 9 - \sqrt{93} }{2} \: and \: x = \frac{ - 9 + \sqrt{93} }{2} are \: the \: roots \: }$

$\boxed{\sf{x=\dfrac{-9+\sqrt{93}}{2} \: and \: x=\dfrac{-9-\sqrt{93}}{2} \: are \: the \: solutions }}$