Mathematics questions
18011 published questions with worked solutions.
- If , are the roots of x^2+px+q=0 and also of x^ 2n +p^nx^n+q^n=0 and if , are the roots of x^n+1+(x+1)^n=0, then n is
- If is a root of the equation 2x(2x+1)=1, then the other root is
- If a(p+q)^2+2bpq+c=0 and a(p+r)^2+2bpr+c=0, then qr=
- p,q,r and s are integers. If the A.M. of the roots of x^2-px+q^2=0 and G.M. of the roots of x^2-rx+s^2=0 are equal, then
- If one root of the equation 8x^2-6x-a-3=0 is the square of the other, then the values of a are
- The sum of the real roots of the equation |x-2|^2+|x-2|-2=0, is
- The number of values of a for which (a^2-3a+2 )x^2+ (a^2-5a+6 )x+a^2-4=0 is an identity in x, is
- If a,b,c are in G.P., then the equations ax^2+2bx+c=0 and dx^2+2ex+f=0 have a common root if da, eb, fc are in
- Let , be the roots of ax^2+bx+c=0, and let ^n+ ^n=S_n for n 1. Then the value of the determinant vmatrix 3&1+S_1&1+S_2...
- If a and b are two distinct real roots of the polynomial f(x) such that a<b, then there exists a real number c lying between a...
- If b and c are odd integers, then the equation x^2+bx+c=0 has
- Let , , , be the roots of x^4+x^2+1=0. Then, the equation whose roots are ^2, ^2, ^2, ^2 is
- If x^2+px+q=0 is the quadratic equation whose roots are a-2 and b-2 where a,b are the roots of x^2-3x+1=0, then
- The roots of ax^2+2bx+c=0 and bx^2-2 ac ,x+b=0 are simultaneously real, then
- If , are the roots of the equation x^2+ ,x+ =0, then the values of and are
- If the equation x^3+ax^2+b=0, b 0 has a root of order 2, then
- If is a root of the quadratic equation x^2+6x-2=0, then another root is
- If , are roots of the equation 375x^2-25x-2=0 and S_n= ^n+ ^n, then _ n _ r=1 ^nS_r is equal to
- For the equation |x|^2+|x|-6=0
- If a and b are the non-zero distinct roots of x^2+ax+b=0, then the least value of x^2+ax+b is