Practice questions
88551 published questions with worked solutions.
- If the roots of the equation 8x^3-14x^2+7x-1=0 are in GP, then the roots are
- If , are the roots of the quadratic equation ax^2+bx+c=0 and k be a real number, then the condition so that <k< is given by
- If and ( < ) are the roots of the equation x^2+bx+c=0 where c<0<b, then
- If the roots of the equation ax^2+bx+c=0 of the form k+1 k and k+2 k+1 , then (a+b+c)^2 is equal to
- Let a,b,c be positive numbers. The following system of equations in x,y and z: x^2 a^2 + y^2 b^2 - z^2 c^2 =1; x^2 a^2 - y^2 b^2...
- The root of the equation 2(1+i)x^2-4(2-i)x-5-3i=0, where i= -1 , which has greater modulus, is
- Let , be the roots of x^2-2x +1=0, then the equation whose roots are ^n, ^n, is
- If the roots of ax^2+bx+c=0 are , and the roots of Ax^2+Bx+C=0 are -k, -k, then B^2-4AC b^2-4ac is equal to
- If x_1,x_2,x_3 are distinct roots of the equation ax^2+bx+c=0, then
- The roots of the equation x^4-8x^2-9=0 are
- If , are the roots of x^2-ax+b=0 and if ^n+ ^n=V_n, then
- If b_1b_2=2 (c_1+c_2 ), then the least one of the equation x^2+b_1x+c_1=0 and x^2+b_2x+c_2=0 has
- The value of x in the given equation 4^x-3^ x- 12 =3^ x+ 12 -2^ 2x-1 is
- If x^2+ax+1 is a factor of ax^3+bx+c, then
- Let p,q 1,2,3,4 . The number of equations of the form px^2+qx+1=0 having real roots, is
- If x is real, the function (x-a)(x-b) (x-c) will assume all real values, provided
- Statement 1: If equations ax^2+bx+c=0, (a,b,c R) and 2x^2+3x+4=0 have a common root, then a:b:c=2:3:4. Statement 2: Roots of...
- If , are the roots of the equation ax^2+bx+c=0 such that < <0, then the quadratic equation whose roots are | |,| |, is given by
- The solution of the quadratic equation (3|x|-3)^2=|x|+7 which belongs to the domain of definition of the function y= x(x-3) are...
- If the roots of the equation 1 x+p + 1 x+q = 1r are equal in magnitude but opposite in sign, then the product of the roots will be