1. Find the value of m such that the equation
x²-2(5+2m)x+3(7+10m) = 0 has equal roots.

2. If a, b are the roots of the equation x²+px+1=0 and c,d are the roots of the equation x²+qx+1=0, show that
q²-p² = (a-c)(b-c)(a+d)(b+d).

3. Find the greatest and the least values of the expression

for real values of x.

4. If the roots of the equation ax²+cx+c=0 be in the ratio m:n, prove that

5. If the equations x²+bx+ca=0 and x²+cx+ab=0 have a common root, show that their roots will satisfy the equation x²+ax+bc=0.