Practice questions
88551 published questions with worked solutions.
- If , , are the roots of the equation x^3+ax^2+bx+c=0, then ^ -1 + ^ -1 + ^ -1 =
- If two equations a_1x^2+b_1x+c_1=0 and a_2x^2+b_2x+c_2=0 have a common root, then the value of (a_1b_2-a_2b_1)(b_1c_2-b_2c_1), is
- If a,b,c R and the equations ax^2+bx+c=0 and x^3+3x^2+3x+2=0 have two roots in common, then
- The equation (a+2)x^2+(a-3)x=2a-1, a -2 has rational roots for
- If 8,2 are the roots of x^2+ax+ =0, and 3,3 are the roots of x^2+ x+b=0, then the roots of x^2+ax+b=0 are
- If , are the roots of x^2+bx-c=0, then the equation whose roots are b and c is
- The roots of the quadratic equation (a+b-2c)x^2-(2a-b-c)x+(a-2b+c)=0 are
- The product of the real roots of the equation |2x+3|^2-3|2x+3|+2=0, is
- If one root of the equation x^2+px+12=0 is 4, while the equation x^2+px+q=0 has equal roots, then the value of q is
- The number of real roots of the equation 2x^4+5x^2+3=0, is
- The roots of the equation (3-x)^4+(2-x)^4=(5-2x)^4 are
- If , are roots of x^2+px-q=0 and , are root of x^2+px+r=0, then the value of ( - )( - ) is
- If , , be the roots of x^3+a^3=0 (a R), then the number of equation(s) whose roots are ( )^2 and ( )^2, is
- If a,b,c are in A.P. and if (b-c)x^2+(c-a)x+a-b=0 and 2(c+a)x^2+(b+c)x=0 have a common root then
- If the equation x^2-3kx+2e^ 2 k -1=0 has real roots such that the product of roots is 7, then the value of k is
- The set of values of p for which the roots of the equation 3x^2+2x+p(p-1)=0 are of opposite signs is
- If x=c is a root of order 2 of a polynomial f(x), then x=c is also a root of the polynomial
- If x R, then the expression 9^x-3^x+1 assumes
- Let f(x) be a quadratic expression which is positive for all real x and g(x)=f(x)+f'(x)+f''(x), then for any real x,
- If A is the A.M. of the roots of the equation x^2-2ax+b=0 and G is the G.M. of the roots of the equation x^2-2bx+a^2=0, then