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Whenever you see a problem involving an inequality (greater than or less than sign) it is really important to pause for a second before you go breaking any rules of mathematics. ...

I would begin the session with checking a basic understanding of the methods of long division, as these will not have been taught very recently. Many students will have been using short division, as it is...

The initial quadratic can be either positive or negative so we must solve for both possibilities.

Solving for positive:

3x^2 - 19x + 20 < 2x + 2    =    3x^2 - 21x + 18 < 0

a) Need to multiply with conjugate to bring z to form a+ib. => z= z * (1-i)/(1-i) = (4-4i) / 2 = 2-2i

b) z^2 = (2-2i)^2 = 4-8i+4 i^2 = 4-8i-4 = 8i

since z is root of x^2+px+q=0 then z* (c...

Expanding out the Brackets: (n²)+ (n² + n + n + 1) + (n² + 2n + 2n +4) = (n²) + (n²+2n+1) + (n²+4n+4) =3n² + 6n +5 Using this r...