Practice questions
88551 published questions with worked solutions.
- If a root of the equation ax^2+bx+c=0 be reciprocal of a root of the equation a'x^2+b'x+c'=0, then
- If , , are the roots of the equation x^3-7x+7=0, then 1 ^4 + 1 ^4 + 1 ^4 is
- Rational roots of the equation 2x^4+x^3-11x^2+x+2=0 are
- The value of a for which the equations x^3+ax+1=0 and x^4+ax^2+1=0 have a common root, is
- If , and are the roots of the equation x^3-3x+1=0, then [ ]+[ ]+[ ] is ([ ] denotes the greatest integer function)
- If 2 ^2 8 is a root of the equation x^2+ax+b=0, where a and b are rational numbers, then a-b is equal to
- Consider the following statements: 1. The equation x^2-cx+d=0 and x^2-ax+b=0 have common root and second equation has equal roots...
- If and are the roots of x^2-x-1=0 and A_n= ^n+ ^n, then AM of A_ n-1 and A_n is
- The number of real roots of the equation e^ x -e^ - x -4=0 are
- The number of real roots of 3^ 2x^2-7x+7 =9 is
- For what value of the sum of the squares of the roots of x^2+(2+ )x- 12(1+ )=0 is minimum?
- 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