Question

solve for the quadratic equation 3x^2 + 8x + 1 = 0​

Answer 1

Answer:

Step by Step Solution

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Step by step solution :

STEP

1

:

Equation at the end of step 1

(3x2 + 8x) - 1 = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 3x2+8x-1

The first term is, 3x2 its coefficient is 3 .

The middle term is, +8x its coefficient is 8 .

The last term, "the constant", is -1

Step-1 : Multiply the coefficient of the first term by the constant 3 • -1 = -3

Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is 8 .

-3 + 1 = -2

-1 + 3 = 2

Observation : No two such factors can be found !!

Answer 2

The answer is  x = (-4+√13)/ 3 and (-4-√13)/ 3

Given:

3x² + 8x + 1 = 0​

To find:

Solve the quadratic equation 3x² + 8x + 1 = 0​

Solution:

Compare given equation with ax² +bx +c = 0

⇒ a = 3, b = 8 and c = 1

As we know discriminant Δ = b² - 4ac

⇒ Δ = (8)² - 4(3)(1) = 64 - 12 = 52

As we know x = (-b ± √Δ)/2a

x = (-8 ± √52)/ 2(3) = -8 ± √4×13 / 6 = -8 ± 2√13 / 6  

⇒ x =  -8 + 2√13 / 6    and  x = -8 - 2√13 / 6  

⇒ x = 2(-4+√13) 6                x = 2(-4-√13)/ 6  

⇒ x = (-4+√13)/ 3                  x = (-4-√13)/ 3  

Therefore, x = (-4+√13)/ 3 and (-4-√13)/ 3  

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