Question

3x^2+6x+3=0 solve the equation using the quadratic formula

Answer 1

Solution

3x² + 6x + 3 = 0

Comparimg the equation with ax² + bx + c = 0

we get,

a = 3 , b = 6 , c = 3

Discriminant = (b)² - 4ac = 0

➙ (6)² - 4(3)(3) = 0

➙ 36 - 36 = 0

➙ 0 = 0

∵ (b)² - 4ac = 0

∴ Two equal roots exist for the following equation.

Roots = $\dfrac{-b}{2a}, \dfrac{-b}{2a}$

= $\dfrac{-6}{2×3}, \dfrac{-6}{2×3}$

= (-1) , (-1)

Answer 2

Given Equation

• 3x² + 6x + 3 = 0

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Solution

• In this question, quadratic formula is used.

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⇛ Firstly we will find the discriminant (D)

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$\star{\boxed{\bf{\orange{D = b^2 - 4ac}}}}$

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Here,

• a = 3
• b = 6
• c = 3

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$\tt\longrightarrow{D = (6)^2 - 4 \times 3 \times 3}$

$\tt\longrightarrow{D = 36 - 36}$

$\tt\longrightarrow{D = 0}$

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• Now, we use the quadratic formula. That is

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$\star{\boxed{\bf{\orange{x = \dfrac{-b \pm \sqrt{D}}{2a}}}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{-(6) \pm \sqrt{0}}{2 \times 3}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{-6 \pm 0}{6}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{-6}{6}}$

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$\mathcal:\implies\: \: \: \: \: \: \: \: {\underline{\boxed{\purple{x = -1}}}}$

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Hence,

• The roots of the given equation are -1 and -1.