Practice questions
88551 published questions with worked solutions.
- In a triangle PQR, R= 2. If ( P2 ) and ( Q2 ) are the roots of ax^2+bx+c=0, a 0, then
- If a,c 0 and , are the roots of the equation ax^2+bx+c=0, then the quadratic equation with 1/ and 1/ as its roots is
- If the roots of the equation x^2-bx+c=0 are two consecutive integers, then b^2-4c is
- If and are the roots of the equation ax^2+bx+c=0 and, if px^2+qx+r=0 has roots 1- and 1- , then r is equal to
- If , be the roots of the quadratic equation x^2+x+1=0, then the equation whose roots are ^ 19 , ^7 is
- If and are the roots of the equation ax^2+bx+c=0, =3 and a,b,c are in AP, then + is equal to
- 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