Find the exact solutions to 6x^2+x+4=0 by using the quadratic formula.
x=-b+-sqrtb^2-4ac/2a
-1+-sqrt1^2-4(6)(4)/2(6)
-1+-sqrt-95/12
-1-95/12
-96/12
x= -8
-1+95/12
94/12= 7.8333..
[-8, 7.83](answer)
do u cumplex numbers???
What do you mean?
do u know cumplex numbers???as your sqrt is negative(b²-4ac=-95) you have to use cumplex numbers to solve this equation
no that's the only way I know how to do it.
so 6x²+x+4=0 has no one solution(no one real solution but there are cumplex solution : it's (-1+-isqrt95)/12
since a=6,b=1,c=4
=-B¡¾¡î(B©÷-4AC)/2A
"-1¡¾¡î(1©÷-4(6)(4))/2(6)
"-1¡¾¡î(-95)/12
so the roots are imaginary
"since the square root of "-1" is "I"
(yes the letter "I")
Then your roots are
"(-1+9.74i)/12 and (-1-9.74i)/12
To find the exact solutions to the quadratic equation 6x^2 + x + 4 = 0 using the quadratic formula, follow these steps:
Step 1: Identify the values of a, b, and c from the equation.
In this case, a = 6, b = 1, and c = 4.
Step 2: Substitute these values into the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Step 3: Evaluate the expression under the square root, which is (b^2 - 4ac):
b^2 - 4ac = (1)^2 - 4(6)(4) = 1 - 96 = -95
Step 4: Simplify the expression under the square root:
sqrt(-95) can be written as sqrt(95) * i, where i is the imaginary unit.
Step 5: Substitute the values back into the quadratic formula and simplify:
x = (-1 ± sqrt(-95)) / (2(6))
= (-1 ± sqrt(95) * i) / 12
Step 6: Separate the two solutions:
x = (-1+ sqrt(95) * i) / 12 and x = (-1 - sqrt(95) * i) / 12
So, the exact solutions to the quadratic equation 6x^2 + x + 4 = 0 are x = (-1+ sqrt(95) * i) / 12 and x = (-1 - sqrt(95) * i) / 12.
Note: i represents the imaginary unit, where i^2 = -1.