Practice questions
88551 published questions with worked solutions.
- a,b and c are all different and non-zero real numbers in arithmetic progression. If the roots of quadratic equation ax^2+bx+c=0...
- If set of values of a' for which f(x)=ax^2-(3+2a)x+6, a 0 is positive for exactly three distinct negative integral values of x...
- Polynomial P(x) contains only terms of odd degree. When P(x) is divided by (x-3), the remainder is 6. If P(x) is divided by...
- If the roots of the cubic, x^3+ax^2+bx+c=0 are three consecutive positive integers. Then the value of a^2 b+1 is equal to
- The quadratic polynomial p(x) has the following properties: p(x) 0 for all real numbers, p(1)=0 and p(2)=2. Find the value of...
- If a and b are positive numbers and each of the equations x^2+ax+2b=0 and x^2+2bx+a=0 has real roots, then the smallest possible...
- Let P(x)=x^3-8x^2+cx-d be a polynomial with real coefficients and with all its roots being distinct positive integers. Then...
- If a^2-4a+1=4, then the value of a^3-a^2+a-1 a^2-1 (a^2 1 ) is equal to
- Let x^2+y^2+xy+1 a(x+y) x,y R, then the number of possible integer(s) in the range of a is
- The quadratic equation x^2+mx+n=0 has roots which are twice those of x^2+px+m=0 and m,n and p 0. Then the value n/p is
- If the equation x^2+2( +1)x+ ^2+ +7=0 has only negative roots, then the least value of equals
- If equation x^4-(3m+2)x^2+m^2=0 (m>0) has four real solutions which are in A.P., then the value of m' is
- All the values of k for which the quadratic polynomial f(x)=-2x^2+kx+k^2+5 has two distinct zeroes and only one of them...
- The solution set of the inequation x+4 x-3 2, is
- The set of values of x satisfying inequations |x-1| 3 and |x-1| 1, is
- The number of integral solutions of x+2 x^2+1 > 12 is
- The solution set of the inequation |x-1|+|x-2|+|x-3| 6, is
- The solution set of the inequation | 2x-1 x-1 |>2, is
- If 2-3x-2x^2 0, then
- The solution set of the inequation 0<|3x+1|< 13, is