Please help me solve: By computing the discriminant.Then determine the number and type of solution for the given equation. 6x^2-5x+5=0  

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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The discriminant of quadratic equation `ax^2 + bx + c = 0` may be computed using the following formula, such that:

`Delta = b^2 - 4ac`

Identifying the coefficients a,b,c yields:

`a = 6, b = -5, c = 5`

Replacing the values of `a,b,c` in expression of Delta yields:

`Delta = (-5)^2 - 4*6*5 => Delta = 25 - 120 => Delta = -95`

Since `Delta` is negative, then there are not real solutions to equation, but there exists two complex conjugate solutions. You may evaluate the solutions using quadratic formula,such that:

`x_(1,2) = (-b+-sqrt Delta)/(2a)`

`sqrt(Delta) = sqrt(-95) = +-i*sqrt 95 (sqrt(-1) = +-i)`

`x_(1,2) = (5+-sqrt(-95))/12`

`x_(1,2) = (5+-i*sqrt(95))/12`

Hence, evaluating the solutions to the given quadratic equation yields 2 complex conjugate solutions `x_(1,2) = (5+-i*sqrt(95))/12.`

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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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`6x^2-5x+5=0 `    use `b^2-4ac`

a=6  b=-5  c=5

`-5^2-4(6)(5)`

25-120= -95    the problem has no real solutions but instead 2 complex solutions

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