## Question

secondary 3 | A Maths

Anyone can contribute an answer, even non-tutors.

##### Rachel

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I'm not sure of how to do part ii but I know part i. please help me! :-)

Date Posted: 5 months ago
Views: 27
J
5 months ago
You probably already know how to find α and β .

Since the roots for b) are 2α + β and α + 2β,

Then (x - (2α + β) )(x - (α + 2β) ) = 0

Sub in the values of α and β directly (or find what are the values of the roots first, then sub in, whichever way you like)

If you didn't know how to find α and β,

then find the sum and product of roots.

Sum = 2α + β + α + 2β
= 3α + 3β
= 3(α + β)
Sub the value of α + β you found in i).

Product = (2α + β)(α + 2β)
= 2α² + 4αβ + αβ + 2β²
= 2(α² + 2αβ + β²) + αβ
= 2(α+β)² + αβ

Sub the values of αβ and α + β in i).

You have found the sum and product,

ax² + bx + c = 0
Divide by a,

x² + b/a x + c/a = 0

We know sum = -b/a and product = c/a
and thus b/a = -sum

So just substitute the values you found into this equation, and multiply accordingly to get your answer