22d- JU Up are real and 0.-B2 are the roots of the equation a²x2 + x + (1 -a) = 0, a > 1, then 82 - 15. 1) a2 2) 1 3) 1 - a2 4)1 + a2 GO

If A_1 and A_2 are two AMs between a and b then (2A_1 -A_2) (2A_2 - A_1) =

If a_1, a_2 are the coefficients of x^n in the expansion of (1+x)^(2n) & (1+x)^(2n-1) respectively then a_1:a_2 will be

Find the condition so that the two equations a_1 x^2+b_1 x+c_1=0 and a_2 x^2+b_2 x+c_2=0 will have a common root.

If the origin lies in the acute angle between the lines a_1 x + b_1 y + c_1 = 0 and a_2 x + b_2 y + c_2 = 0 , then show that (a_1 a_2 + b_1 b_2) c_1 c_2 lt0 .

If a_1 and a_2 are two non-collinear unit vectors and if |a_1+a_2|=sqrt(3) , then the value of (a_1-a_2)*(2a_1+a_2) is

If 1, a_1,a_2,a_3 ,…, a_(n-1) are the nth roots of unity then prove that : 1+a_1+a_2+…+a_(n-1) =0.

Illustration 1.2 Find the set of all possible real values of a such that the inequality (x (a 1) (x (a2 2) 0 holds for all x E (-1,3)