A-level Maths Question

Could someone please explain why for part (b) you can't just use your calculator to find the root? It just gives a decimal, but then when you find the root from the quadratic after dividing by the factor, it doesn't give a decimal but gives it in surd form. Why is that? Thanks.

It asks for an exact answer. So a decimal would be an approximation of the irrational surd.

Yes but solving the quadratic using my calculator gives it on exact surd form, whereas solving the cubic one gives it in decimal. So that’s why you have to divide by the (2x-1) factor. But why is that?

Yes but solving the quadratic using my calculator gives it on exact surd form, whereas solving the cubic one gives it in decimal. So that’s why you have to divide by the (2x-1) factor. But why is that?

Are you asking why doesnt your calculator give an exact (surd) answer to a cubic? The question asks for all stages of algebra/working, so even if your calculator did give the root(s) it wouldnt gain the marks.

Oh ok, so is it because you can only use the quadratic formula (which is what the calculator does) on a quadratic, and therefore that is why you need a quadratic? I just want to understand why you need to do that, so I can see to know to do it in the future.

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Ok here it is

Oh ok, so is it because you can only use the quadratic formula (which is what the calculator does) on a quadratic, and therefore that is why you need a quadratic? I just want to understand why you need to do that, so I can see to know to do it in the future.