Maths Olympiad Exam Numerical Ability

for what value of m the equation 2mx^2-2(1+2m)x+(3+2m)=0 have equal roots

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for quadratic equation (1+2m)^2=(3+2m)(2m) :-(AX^2-2AXB+B^2)
1+4m^2+4m=6m+4m
2m=1
m=1/2
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Maths Olympiad Other Question

determine the value of p for which the quadratic equation 2x^2+px+8=0 has real roots if x1,x2,x3...................xn are in AP then 1/x1x2+1/x2x3+................+1/x(n-1)xn is equal to
a)(n+1)/x1
b)(n-1)/x2
c)(n-1)/x1xn
d)(n+1)x1x2