If $k$ is a multiple of 4, which of the following is NOT a possible root of $x^2-6x+k=0$ ?

Correct answer marked below

Correct

3-\sqrt{5}

3+\sqrt{5}

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Comments

GuilhermeJun 30

Wait, how do we use the fact that k is a multiple of 4? I plugged in the choices but wasn't sure what condition to check. Can someone nudge me?

EricJul 8

Yeah, the constant term is the product of the roots. That's the key.

AnusreeJul 22

Got it after realizing the product of roots = k. Since k is a multiple of 4, the product must be divisible by 4. Checking each pair works fast.

RohitAug 26

This one was medium for me. The radicals in B and E looked scary, but once you remember sum/product of roots it's fine. Nice question.

HrishitaSep 4

Same, I almost started using the quadratic formula before seeing the trick.

NaderJun 8

Is k supposed to be a positive multiple of 4, or could it be negative? The wording just says multiple of 4 and that tripped me up a bit.

PrabhjotJun 11

Good point, but I think the divisibility check still gives the same answer either way.

What this question tests

Your handling of square and higher roots, including simplifying radicals.

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.

If kkk is a multiple of 4, which of the following is NOT a possible root of x2−6x+k=0x^2-6x+k=0x2−6x+k=0?