Hi can any body solve this question?

The equation 2x²-4x-3=0 has roots a and b. Find the quadratic equation with integer coefficients and with roots a³ , b³

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- Sep 29th 2008, 09:07 AMdjmccabiefurther maths roots of equations
Hi can any body solve this question?

The equation 2x²-4x-3=0 has roots a and b. Find the quadratic equation with integer coefficients and with roots a³ , b³ - Sep 29th 2008, 09:44 AMwisterville
Hello,

Using Viete, you know the values of a+b and ab.

Since a^3+b^3=(a+b)^3-3ab(a+b), you know the values of p=a^3+b^3 and q=a^3b^3.

The quadratic equation with roots a^3, b^3 is x^2-px+q=0.

Arrange it so that it has integer coefficients.

Bye. - Sep 29th 2008, 10:04 AMSoroban
Hello, djmccabie!

Quote:

The equation has roots and

Find the quadratic equation with integer coefficients and with roots

Hence: .

Cube [1]: .

. . Hence: .

Cube [2]: .

Therefore, the equation is: .

- Sep 29th 2008, 11:22 AMdjmccabie
Thanks alot soroban! really helped i had the right idea just got a few signs wrong (Shake)