# Remember

- If a + b + c = 0, then a
^{3}+ b^{3}+ c^{3}= 3abc

Example

If the roots of the equation 2

*x*^{2}+ 8*x*+*m*^{3}= 0 are equal, find the value of*m*.Solution

If the roots are equal, then

*b*^{2}â€“ 4*ac*= 0.

Example

If

*a*,*b*are the roots of the equation 2*x*^{2}â€“ 4*x*â€“ 3 = 0, find*a*+*b*and*ab*.Solution

From the equation

we know that

*a*= 2,*b*= â€“4,*c*= â€“3,we know that

Example

Find the roots of the equation

*x*^{2}â€“ 8*x*+ 12 = 0.Solution

From the equation, we have

The roots can be found by the relation,

*a*= 1,*b*= â€“8,*c*= 12The roots can be found by the relation,

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