Practice questions
88551 published questions with worked solutions.
- The cubic equation whose roots are thrice to each of the roots of x^3+2x^2-4x+1=0 is
- If the sum of the roots of the equation ax^2+2x+3a=0 is equal to their products, then the value of a is
- If , and are the roots of the equation x^3-8x+8=0, then ^2 and 1 are respectively
- If and are the roots of the equation ax^2+bx+c=0, then (1+ + ^2 ) (1+ + ^2 ) is equal to
- If and are the roots of the equation px^2+qx+r=0, then
- The value of a for which one root of the quadratic equation (a^2-5a+3 )x^2+(3a-1)x+2=0 is twice as large as the other, is
- If a,b and c are in geometric progression and the roots of the equation ax^2+2bx+c=0 are and and those of cx^2+2bx+a=0 are and ,...
- If 3p^2=5p+2 and 3q^2=5q+2 where p q, then the equation whose roots are 3p-2q and 3q-2p is
- Let , be the roots of equation 2x^2-(p+1)x+(p-1)=0. If - = , then what is the value of p?
- Suppose that two persons A and B solve the equation x^2+ax+b=0. While solving A commits a mistake in the coefficient of x was...
- If and are imaginary cube roots of unity, then ^4+ ^4+ 1 is equal to
- If and are the roots of x^2-2x+4=0, then the value of ^6+ ^6 is
- If , are the roots of the equation ax^2+bx+c=0, then the equation whose roots are 2 +3 and 3 +2 , is
- Let , ^2 be the roots of x^2+x+1=0, then the equation whose roots are ^ 31 , ^ 62 is
- If , , are the roots of x^3+2x^2-3x-1=0, then ^ -2 + ^ -2 + ^ -2 is equal to
- Let f(x)=ax^2+bx+c, a 0 and =b^2-4ac. If + , ^2+ ^2 and ^3+ ^3 are in GP, then
- If and cosec are the roots of the equation x^2-px+q=0, then
- If + =4 and ^3+ ^3=44, then , are the roots of the equation
- Given that A and B are the roots of x^2-px+q=0, then the value of ^2(A+B) is
- If and are the solutions of the quadratic equation ax^2+bx+c=0 such that = ^ 1/3 , then