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junior college 1 | H2 Maths
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farhan sadik
Farhan Sadik

junior college 1 chevron_right H2 Maths chevron_right Singapore

How to do part 3 and 4 (iii and iv)?

Date Posted: 4 years ago
Views: 261
J
J
4 years ago
iv)


f(2) = (a(2) + b)² = (2a + b)²


When ff(2) = b²,

(a(2a+b)² + b)² = b²

(a(2a + b)² + b)² - b² = 0

(a(2a + b)² + b - b)(a(2a + b)² + b + b) = 0


a(2a + b) = 0 or a(2a + b)² + 2b = 0

a = 0 or b = -2a


or

4a³ + 4a²b + ab² + 2b = 0

ab² + (4a² + 2)b + 4a³ = 0

b = [-(4a² + 2)± √( (4a² + 2)² - 4(a)(4a³) ) ] / 2a

b = [-(4a² + 2) ± √(16a⁴ + 16a² + 4 - 16a⁴)] / 2a

b = [-(4a² + 2) ± √(16a² + 4) ] / 2a

b = [-(4a² + 2) ± 2√(4a² + 1)] / 2a

b = -2a - [1± √(4a² + 1)] / a
farhan sadik
Farhan Sadik
4 years ago
(^^)
J
J
4 years ago
Same answer as answer key?
farhan sadik
Farhan Sadik
4 years ago
The answer key says no answer
farhan sadik
Farhan Sadik
4 years ago
I think the values that you got should be rejected as a and b are always positive. So there is indeed no answer.
J
J
4 years ago
That was my thinking at first too. So yea just reject the answer and quote the relevant reason

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Lala Chew
Lala Chew's answer
12 answers (Tutor Details)
1st
farhan sadik
Farhan Sadik
4 years ago
Sorry to tell you, but you sent your answer to a wrong person.
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farhan sadik
Farhan Sadik's answer
1 answers (A Helpful Person)
So the answer is this?
The answer key says no answer
J
J
4 years ago
You should be able to stop at the 3rd step by stating that since a and b > 0, the expression > 0 since all terms of it are positive , therefore no solution
farhan sadik
Farhan Sadik
4 years ago
Extra working for extra marks!
J
J
4 years ago
Some inaccuracies in the one shown here though. Follow the one I posted
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Lim En Jie
Lim En Jie's answer
73 answers (Tutor Details)
Can expand as given if you are confident but waste time and mistake prone (ie skip let A=(ax+b)^2 and just solve the whole equation).

Can don’t be A if it’s confusing can be C/D/E/F etc.
farhan sadik
Farhan Sadik
4 years ago
So, how did you do iv?
The part 3 I can understand though.
Lim En Jie
Lim En Jie
4 years ago
Follow the steps at the bottom of the page where it goes:
“Given ff(x)=b^2” and
“let A=(ax+b)^2”

If still cannot understand, I’ll post the workings.
J
J
4 years ago
ff(2) actually, not ff(x)
Lim En Jie
Lim En Jie
4 years ago
Ah okay my bad