Question

What are the solutions of the equation 6x2 +5x+1 = 0 ?

Answer 1

Step-by-step explanation:

6x^2+5x+1=0

Descr= b^2-4ac

Descr= 25-24=1

X1= (-b+√descr)/2a = (-5+1)/12= -1/3

X2= (-b-√descr)/2a = (-5-1)/12= -1/2

Answer 2

see explanation

Explanation:

Given

6x² + 5x + 1 = 0

To factorise the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

The factors are + 3 and + 2

Use these factors to split the x- term

6x² + 3x + 2x + 1 = 0 ← ( factor the first/second and third/fourth terms )

3x(2x + 1) + 1 (2x + 1) = 0 ← factor out (2x + 1) from each term

(2x 1)(3x + 1) = 0

Equate each factor to zero and solve for x

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = -
`(1)/(2)`

3x + 1 = 0 ⇒ 3x = - 1 ⇒ x = -
`(1)/(3)`