Practice questions
88551 published questions with worked solutions.
- E_1: a+b+c=0, if 1 is a root of ax^2+bx+c=0, E_2: b^2-a^2=2ac, if , are the roots of ax^2+bx+c=0. Which of the following is true?
- If , are the roots of the equation (x-a)(x-b)=5, then the roots of the equation (x- )(x- )+5=0 are
- The polynomial (ax^2+bx+c ) (ax^2-dx-c ), ac 0 has
- If (x-2) is a common factor of the expressions x^2+ax+b and x^2+cx+d, then b-d c-a is equal to
- If the equation (a+1)x^2-(a+2)x+(a+3)=0 has roots equal in magnitude but opposite in sign, then the roots of the equation are
- The number of real roots of f(x)=0, where f(x)=(x-1)(x-2)(x-3)(x-4) lying in the interval (1,3) is
- The roots of the equation (q-r)x^2+(r-p)x+(p-q)=0 are
- If the cube root of unity are 1, , ^2, then the roots of the equation (x-1)^3+8=0, are
- The maximum number of real roots of the equation x^ 2n -1=0 is
- If b^2 4ac for the equation ax^4+bx^2+c=0, then all the roots of the equation will be real positive of
- The number of real solution of the equation ( 9 10 )^x=-3+x-x^2 is
- If the cube roots of unity are 1, , ^2, then the roots of the equation (x-2)^3+27=0 are
- The number of real roots of the equation (x+ 1x )^3+x+ 1x=0 is
- Both the roots of the given equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are always
- The solution of the equation 2x^3-x^2-22x-24=0 when two of the roots in the ration 3:4, is
- The roots of |x-2|^2+|x-2|-6=0 are
- The values of x and y that satisfy the equation (x,y real numbers) x^2-xy+y^2-4x-4y+16=0 is
- The number of real roots of the equation x^4+ x^4+20 =20 is
- If 32+ 72i is a solution of the equation ax^2-6x+b=0, where a and b are real numbers, then value of a+b is equal to
- The roots of (x-a)(x-a-1)+(x-a-1)(x-a-2)+(x-a)(x-a-2)=0, a R are always