For what value of λ the sum of the squares of the roots of x2+(2+λ)x−12(1+λ)=0 is minimum
3/2
1
1/2
11/4
If the roots of the equation 8x3−14x2+7x−1=0 are in G.P., then the roots are
If a,b,c,d and p are distinct real numbers such that (a2+b2+c2)p2−2p(ab+bc+cd)+(b2+c2+d2)≤0, then
Let a,b be non-zero real numbers. Which of the following statements about the quadratic equation ax2+(a+b)x+b=0 is necessarily true?
I. It has at least one negative root.
II. It has at least one positive root.
III. Both its roots are real.
Consider the following two statements
I. Any pair of consistent liner equations in two variables must have a unique solution.
II. There do not exist two consecutive integers, the sum of whose squares is 365.Then,
Let x1,x2,x3∈R−{0} ,x1+x2+x3≠0 and 1x1+1x2+1x3=1x1+x2+x3, then 1xn1+xn2+xn3=1xn1+1xn2+1xn3 holds good for