JEE Main questions
34495 published questions with worked solutions.
- If , , are the roots of the equation x^3-6x^2+11x-6=0, then ^2 + is equal to
- If the roots of the equation 4x^3-12x^2+11x+k=0 are in arithmetic progression, then k is equal to
- If , and are the roots of equation x^3-3x^2+x+5=0, then y= ^2+ satisfies the equation
- Let p and q be real numbers such that p 0, p^3 q and p^3 -q. If and are non-zero complex numbers satisfying + =-p and ^3+ ^3=q,...
- Let the two numbers have arithmetic mean 9 and geometric mean 4. Then, these numbers are the roots of the quadratic equation
- If and are the roots of x^2+5x+4=0, then the equation whose roots are +2 3, +2 3 is
- If one root of the equation x^2+px+q=0 is 2+ 3, then the value of p and q respectively
- If the sum of the roots of the quadratic equation ax^2+bx+c=0 is equal to the sum of the square of their reciprocals, then ac, ba...
- The , are the roots of the equation x^2+ax+b=0, then 1 ^2 + 1 ^2 is equal to
- If the roots of the equation x^2+px+q=0 are 30^ and 15^ respectively, then the value of 2+q-p is
- For the equation 1 x+a - 1 x+b = 1 x+c , if the product of the roots is zero, then the sum of the roots is
- If , be the roots of x^2-a(x-1)+b=0, then the value of 1 ^2-a + 1 ^2-a + 2 a+b is
- If , , are the roots of the equation x^3+4x-1=0, then ( + )^ -1 +( + )^ -1 +( + )^ -1 is equal to
- If one root of the equation lx^2+mx+n=0 is - 92 (l, m and n are positive integers) and m 4n = lm, then l+n is equal to
- 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