Quadratic equationsShow how to find the solution for the following quadratic equations, using quadratic formula: 3x^2 + 9x - 27 = 0  

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The quadratic formula for a general queadratic equation ax^2 + bx + c = 0 gives the roots as x1 = -b/2a + sqrt(b^2 - 4ac)/2a and x2 = -b/2a - sqrt(b^2 - 4ac)/2a

Here, the equation is 3x^2 + 9x - 27 = 0

x1 = -9/6 + sqrt (81 + 4*27*3)/6 = -3/2 + (sqrt 405)/6

=> -3/2 + (3*sqrt 5)/2

x2 = -3/2 - (3*sqrt 5)/2

The solutions of the equation is -3/2 + (3*sqrt 5)/2 and -3/2 - (3*sqrt 5)/2

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To calculate the roots of the quadratic, we'll use the quadratic formula:

x1 = [-b+sqrt(b^2 - 4ac)]/2a

x2 = [-b-sqrt(b^2 - 4ac)]/2a

Where a,b,c are the coefficients of the quadratic.

We'll identify a,b,c:

a = 3

b = 9

c = -27

We'll substitute them into the formula:

x1 = [-9+sqrt(81 + 324)]/6

x1 = (-9+sqrt405)/6

x1 = 9(-1 + sqrt5)/6

x1 = 3(-1+sqrt5)/2

x2 = 3(-1-sqrt5)/2

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