Practice questions
88551 published questions with worked solutions.
- 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
- Statement 1: If both roots of the equation 2x^2-x+a=0 (a R) lies in (1,2), then -1<a 18. Statement 2: If F(x)=2x^2-x+a, then D 0,...
- If each pair of the equation x^2+ax+b=0, x^2+bx+c=0 and x^2+cx+a=0 has a common root, then product of all common roots is
- Statement 1: If both roots of the equation 4x^2-2x+a=0, a R lie in the interval (-1,1), then -2<a 14. Statement 2: If...
- The number of real solutions of the equation |x^2+4x+3 |+2x+5=0 are
- Number of integer roots of the equation (x+2)(x+3)(x+8)(x+12)=4x^2 is
- If the equation 2x^2+3x+5 =0 and x^2+2x+3 =0 have a common root, then is equal to
- If roots of x^2-ax+b=0 are prime numbers, then
- The equation x^ 34( _2x)^2+( _2x)- 54 = 2 has
- If the roots of the equation qx^2+px+q=0 are complex, where p,q are real, then the roots of the equation x^2-4qx+p^2=0 are