You would Factorise!

Algebra Level 2

The roots of the equation x^2 + 4x - 5 = 0 is also roots of 2x^3 + 9x^2 - 6x - 5 = 0. Find the third root.

Provide answer in decimal.


The answer is -0.5.

Dev Sharma by Dev Sharma , 20, India

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2 solutions

Simplest solution is just to divide 2 x 3 + 9 x 2 − 6 x − 5 b y x 2 + 4 x − 2 2x^3+9x^2-6x-5 \quad by \quad x^2+4x-2 .

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Dev Sharma
Aug 20, 2015

Let the roots be a,b,c.

Then in quadratic equation, we get a + b = -4.

And in cubic, a + b + c = -9/2

Thus, c = -1/2 = -0.5

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