Mathematics questions
18011 published questions with worked solutions.
- If and be the roots of the equation 2x^2+2(a+b)x+a^2+b^2=0, then the equation whose roots are ( + )^2 and ( - )^2, is
- The number which exceeds its positive square roots by 12, is
- If x is real, then the maximum and minimum values of the expression x^2-3x+4 x^2+3x+4 will be
- Consider the following statements: 1. If the ratio of roots of the quadratic equation ax^2+bx+c=0 be p:q, then pqb^2=(p+q)^2ac....
- Consider the following statements: 1. If the quadratic equation is ax^2+bx+c=0 such that a+b+c=0, then roots of the equation...
- Let a,b,c be real number a 0. If is a root of a^2x^2+bx+c=0, is a root of a^2x^2-bx-c=0 and 0< < , then the equation...
- If the roots of the equation ax^2+bx+c=0 be and , then the roots of the equation cx^2+bx+a=0 are
- The values of a for which 2x^2-2(2a+1)x+a(a+1)=0 may have one root less than a and other root greater than a are given by
- The values of a' for which (a^2-1 )x^2+2(a-1)x+2 is positive for any x, are
- If roots of the equation ax^2+bx+c=0; (a,b,c N) are rational numbers, then which of the following cannot be true?
- If (ax^2+c )y+ (dx^2+c' )=0 and x is a rational function of y and ac is negative, then
- If x,y,z are real and distinct, then u=x^2+4y^2+9z^2-6yz-3zx-2xy is always
- How many roots of the equation x- 1 x-1 =1- 2 x-1 have?
- If , be the roots of the equation x^2-px+q=0 and _1, _1 be the roots of the equation x^2-qx+p=0, then the equation whose roots...
- If p(x)=ax^2+bx+c and Q(x)=-ax^2+dx+c, where ac 0, then P(x)Q(x)=0 has at least
- If the difference of the roots of the equation x^2-bx+c=0 be 1, then
- Let , be the roots of the equation x^2-x+p=0 and , be the roots of x^2-4x+q=0. If , , , are in GP, then integral values of p,q...
- If , are the roots of the equation ax^2+bx+c=0, then the equation whose roots are + 1 and + 1 is
- The roots of the equation |2x-1|^2-3|2x-1|+2=0 are
- The number of solutions of 5+ (x^2+1 ) (x-2) =2 is