Question

solve the given quadratic equation x^2-3(x+3)=0 giving your answer correct to two decimal places​

Answer 1

EXPLANATION.

Quadratic equation,

⇒ x² - 3(x + 3) = 0.

As we know that,

⇒ x² - 3x - 9 = 0.

D = discriminant

⇒ D = b² - 4ac.

Put the values in equation, we get.

⇒ D = (-3)² - 4(1)(-9).

⇒ D = 9 + 36.

⇒ D = 45.

⇒ x = -b ±√D/2a.

⇒ x = -b + √D/2a  and  x = -b - √D/2a.

⇒ x = -(-3) + √45/2.

⇒ x = 3 + √45/2.

⇒ x = 3 + 3√5/2.

⇒ x = 3(1 + √5)/2.

⇒ x = -(-3) - √45/2.

⇒ x = 3 - 3√5/2.

⇒ x = 3(1 - √5)/2.

Answer 2

$\large\underline\purple{\bold{Solution :- }}$

$\tt \ \: :  ⟼ {x}^{2} - 3(x + 3) = 0$

$\tt \ \: :  ⟼ {x}^{2} - 3x - 9 = 0$

$\tt \:  ⟼ On \: comparing \: with \: {ax}^{2} + bx + c = 0 \: we \: get$

$\tt \ \: :  ⟼ a \: = 1 \: \\ \tt \ \: :  ⟼ b = - 3 \\ \tt \ \: :  ⟼ c \: = - 9$

$\tt \ \: :  ⟼ Now, \:discriminant \: d \: = {b}^{2} - 4ac$

$\tt \ \: :  ⟼ \:d \: = {( - 3)}^{2} - 4 \times 1 \times ( - 9)$

$\tt \ \: :  ⟼ d = 9 + 36$

$\tt\implies \:d \: = \: 45$

☆ Solution of quadratic equation is given by

$\tt \ \: :  ⟼ x = \dfrac{ - b \: \pm \: \sqrt{d} }{2a}$

$\tt \ \: :  ⟼ x \: = \dfrac{ - ( - 3) \: \pm \: \sqrt{45} }{2 \times 1}$

$\tt \ \: :  ⟼ x = \dfrac{3 \: \pm \: 3 \sqrt{5} }{2}$

$\tt \:  ⟼ x = \dfrac{3 \: \pm \: 3 \times 2 .236}{2}$

$\tt \ \: :  ⟼ x = \dfrac{3 \: \pm \: 6.708}{2}$

$\tt \ \: :  ⟼ x = \dfrac{3 + 6.708}{2} \: or \: \dfrac{3 - 6.708}{2}$

$\tt \ \: :  ⟼ x = \dfrac{9.708}{2} \: or \: \dfrac{ - 3.708}{2}$

$\tt \ \: :  ⟼ x = 4.85 \: or \: - 1.85$