Practice questions
88551 published questions with worked solutions.
- If the roots of the equation 3x^2-6x+5=0 are and , then the equation whose roots are + and 2 + will be
- The quadratic equation in x such that the arithmetic mean of its roots is 5 and geometric mean of the roots is 4, is given by
- If x^2+px+q=0 has the roots and , then the value of ( - )^2 is equal to
- If one root of equation x^2+ax+12=0 is 4 while the equation x^2+ax+b=0 has equal roots, then the value of b is
- If , are the roots of the equation lx^2+mx+n=0, then the equation whose roots are ^3 and ^3, is
- If , , are the roots of x^3-2x^2+3x-4=0, then the value of ^2 ^2+ ^2 ^2+ ^2 ^2 is
- The value of a for which the sum of the squares of the roots of the equation x^2-(a-2)x-a-1=0 assumes the least value, is
- The condition that x^3-px^2+qx-r=0 may have two of its roots equal in magnitude but opposite sign, is
- Let , be the roots of the equation x^2-ax+b=0 and A_n= ^n+ ^n. Then A_ n+1 -aA_n+bA_ n-1 is equal to
- If and are the roots of the equation x^2-7x+1=0, then the value of 1 ( -7)^2 + 1 ( -7)^2 is
- If , are the roots of the equation 6x^2-5x+1=0, then the value of ^ -1 + ^ -1 is
- If the sum of two of the roots of x^3+px^2-qx+r=0 is zero, then pq is equal to
- If a and b are the roots of the equation x^2+ax+b=0, a 0, b 0, then the values of a and b are respectively
- If , are the roots of the equation ax^2+bx+c=0, then a +b + a +b is equal to
- If _1, _2, _3, _4 are the roots of the equation x^4+ (2- 3 )x^2+2+ 3=0, then the value of (1- _1)(1- _2)(1- _3)(1- _4) is
- If the difference between the roots of x^2+ax-b=0 is equal to the difference between the roots of x^2-px+q=0, then a^2-p^2 in...
- If , are the roots of the equation ax^2+bx+c=0, then the value of 1 a +b + 1 a +b is equal to
- The quadratic equation whose roots are ^218^ and ^236^ is
- If + =-2 and ^3+ ^3=-56, then the quadratic equation whose roots are and is
- If the sum of the roots of the equation ax^2+bx+c=0 be equal to the sum of the reciprocal of their squares, then bc^2,ca^2,ab^2...