solve 24x^3-52x^2-60x=0

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neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve 24x^3 -52x^2-60x = 0

We divide the both sides by 4x.

6x^2 -13x -15 = 0

We split the middle term -13x = -18x +5x  in such a way that thr product -18x*5x = product of end terms  equals 6x^2*(-15).

6x^2-18x+5x-15 = 0

6x(x-3) +5(x-3) = 0

(x-3)(6x+5) = 0

Therefore the given  equation now becomes:

4x(x-3)(6x+5) = 0

x= 0  or x-3 = 0 or 6x+5 = 0

x = 0  or x = 3 or x = -5/6

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The equation will have 3 roots, since the maximum order of polynomial is 3.

We'll factorize by x and we'll get:

x(24x^2 - 52x - 60) = 0

We'll set each factor as zero:

x1 = 0

and

24x^2 - 52x - 60 = 0

We'll divide by 4:

6x^2 - 13x - 15 = 0

We'll apply the quadratic formula:

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

x1 = [13+sqrt(169+360)]/12

x1 = (13+23)/12

x1 = 3

x2 = (13-23)/12

x2 = -10/12

x2 = -5/6

The roots of the equation are: {-5/6 , 0 , 3}.

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