Hello ,
Can anyone tell me how to solve this one?
I couldn’t understand the video solution posted by greg there.
Hint: there is actually more information than what’s required to solve the problem, however the extra information (the “one more root” part) still helps.
Also: the equation is a cubic but you have two different roots. What could this mean?
A cubic polynomial should have 3 roots
If there is only one more root then it means the other 2 roots are repeated right?
Oh ok so we can write it like
(X-3)(x-a)^2 right?
If this is true, I still didn’t get the next part on how to get the value
You can just divide the equation by (x-3) and you’ll end up with a quadratic equation which on factorising will take the form (x-a)^2
Division of equations
That isn’t necessary. Hint: selectively expand (x - 3)(x - a)2 and get a.
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An easy way to do this would be to use the polynomial property:
Given a polynomial f(x), the constant will be the product of all roots.
They’ve already given 3 as one root, the other two are the same. Thus 3xx = 12
Thus, x would be 2.
The standard equation for cubic polynomial (where the constants are written in terms of roots) should give you a better idea:
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