Maths A-level questions…please help!?
ok im trying to do my homework…i’ve done parts of questions but cant do the second bits to them..please help!
1) The equation x^2+5kx+2k=0, where k is a constant, has real roots.
write down the values of k for which the equation x^2+5kx+2k=0 has equal root.
2) solve the simultaneous equations:
x=2y-2
x^2=y^2+7
3) find the coordinates of the vertex of the curve y=4x^2-12x+15 and sketch the curve
thanks 
x
3) dy/dx = 8x-12; At vetex, dy/dx = 0, Hence 8x-12 = 0.
8x = 12,
x = 12/8 =1.5
y = 9-18+15 =6
The vertex is at (6, 1.5)
sorry,annot sketch curve here….
but it looks like a U the the left line crossing the y-axis at y=15, and has a minimum vertex at x=6,y=1,5, at which point, the gradient = 0, and the gradient change from – to + …..then curves upwards…..
2)
(2y-2)^2 = 4y^2 -8y + 4
4y^2 – 8y +4 = y^2 + 7
3y^2 = 3
y^2 = 1, y = +1 or -1
so, x=0, or – 4
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