help with quadratic function (1 Viewer)

BadBoo · Aug 30, 2012

Hey guys, can you please help me with this question:
If a and B are the roots of the quadratic equation 2x^2+4x-5=0, evaluate a^3+b^3.

Thanks!

Carrotsticks · Aug 30, 2012

RealiseNothing · Aug 30, 2012

Alternative way:

Multiply both sides by 'x':

$2x^3 + 4x^2 - 5x = 0$

Since A and B are roots:

$2A^3 + 4A^2 - 5A = 0$

$2B^3 + 4B^2 - 5B = 0$

Solve simultaneously:

$2A^3 + 2B^3 = - 4A^2 - 4B^2 + 5(A+B)$

$A^3 + B^3 = \frac{5}{2}(A+B) - 2A^2 - 2B^2$

$A^3 + B^3 = \frac{5}{2}(A+B) - 2(A^2 + B^2)$

Now we want to find $A^2 + B^2$

Using sums and products of roots:

$(A + B)^2 = A^2 + B^2 + 2AB$

$(-2)^2 = A^2 + B^2 - 5$

$A^2 + B^2 = 9$

Also note that:

$A + B = -2$

Sub this into the other expression we got:

$A^3 + B^3 = -5 - 2(9)$

$A^3 + B^3 = -23$

Let's hope I didn't typo this time.....

BadBoo · Aug 30, 2012

Thank you very much!

help with quadratic function (1 Viewer)

BadBoo

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Carrotsticks

Retired

RealiseNothing

what is that?It is Cowpea

BadBoo

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