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FP1 question

for part B, i expanded (x-2)(x-(5-2i))(x-(5+2i)) and got many terms, but managed to get the right answer. I am wondering if i can do this in the exam and still get full marks for this question?

Reply 1

Zacken

Original post by alesha98

for part B, i expanded (x-2)(x-(5-2i))(x-(5+2i)) and got many terms, but managed to get the right answer. I am wondering if i can do this in the exam and still get full marks for this question?

Yes, of course.

Reply 2

natninja

Original post by alesha98

for part B, i expanded (x-2)(x-(5-2i))(x-(5+2i)) and got many terms, but managed to get the right answer. I am wondering if i can do this in the exam and still get full marks for this question?

I believe that is a valid way of solving this and should still get you full marks.

(x - 2)(x - (5 - 2i))(x - (5 + 2i)) = 0[br](x - 2)(x^2 - x(5 - 2i) - x(5 + 2i) + (5 - 2i)(5 + 2i)) = 0[br](x - 2)(x^2 - 10x + 29) = 0[br]x^3 - 10x^2 + 29x - 2x^2 + 20x - 58 = 0[br]x^3 - 12x^2 + 49x - 58 = 0

Reply 3

alesha98

Original post by Zacken

Yes, of course.

But in the mark scheme, it expanded (x-(5-2i))(x-(5+2i)) first. But i expanded (x-2)(x-(5-2i)) first, and would i lose a mark because there is a mark for the (3 terms quadratic equation )(x-2) ?

Reply 4

natninja

Original post by alesha98

But in the mark scheme, it expanded (x-(5-2i))(x-(5+2i)) first. But i expanded (x-2)(x-(5-2i)) first, and would i lose a mark because there is a mark for the (3 terms quadratic equation )(x-2) ?

Depends what the letter next to the marks value was, if it was an M mark you could well still get it. If it was an A mark or D (I think, could be S or E?) you wouldn't get it. That would be for edexcel at any rate.

Reply 5

Zacken

Original post by alesha98

But in the mark scheme, it expanded (x-(5-2i))(x-(5+2i)) first. But i expanded (x-2)(x-(5-2i)) first, and would i lose a mark because there is a mark for the (3 terms quadratic equation )(x-2) ?

No, of course not...

(x-2)(x-(5-2i)) is still going to result in a quadratic. Nobody cares about the order you expand things in.

Reply 6

alesha98

Original post by Zacken

No, of course not...

(x-2)(x-(5-2i)) is still going to result in a quadratic. Nobody cares about the order you expand things in.

Thankyou so much, i dont want to lose any silly marks ...

Reply 7

alesha98

Original post by natninja

ok thankyou, it is a M :smile:

Reply 8

natninja

Original post by alesha98

ok thankyou, it is a M :smile:

Should be fine then, the mark should in theory be for expanding it out whichever way (though there is a possibility that it is for noting that an expansion by doing the complex bits first is simpler...)

Reply 9

Zacken

Original post by natninja

(though there is a possibility that it is for noting that an expansion by doing the complex bits first is simpler...)

Not so. Any valid mathematical method will earn credit. You are overestimating the rigidity of the markscheme.

Reply 10

circuits4life

Original post by alesha98

for part B, i expanded (x-2)(x-(5-2i))(x-(5+2i)) and got many terms, but managed to get the right answer. I am wondering if i can do this in the exam and still get full marks for this question?

quicker approach:

•

Let us say you have a general quadratic x²+bx+c where b² -4c<0 & the quadratic's roots are α & β

•

then we know x²+bx+c≡ (x-α )(x-β )

•

therefore, if expand (x-α )(x-β ) we get x²-(α+β)x+αβ now if you let α=λ+iμ then β=λ-iμ we can do this because the coefficients of quadratic are always real in fp1 therefore complex roots occur in pairs.

•

α+β=2λ and αβ=λ²+μ²

•

now we get to the important form: x²+bx+c≡x²-2λx+(λ²+μ²)

now let us apply this to your question; x=5±i2 therefore by using the form above the following quadratic x^2-10x+29 will give us these roots now we can say (x-2)(x²-10x+29)≡x³-12x²+cx+d then we compare coefficients for x⁰& x and get d=-2*29=-58 & c=29+20=49 this took about 1.5min alot quicker then

Reply 11

natninja

Original post by Zacken

Not so. Any valid mathematical method will earn credit. You are overestimating the rigidity of the markscheme.

I remember that when I did it 4 years ago there were 1-3 marks per paper that were for writing out a specific expression and that otherwise any method would be fine. I also remember that if you just wrote the answer you didn't get any method marks - that's the thing I like about university, if I write the correct answer I get full marks.