Mathematics questions
18011 published questions with worked solutions.
- 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
- The common roots of the equations x^3+2x^2+2x+1=0 and 1+x^ 2002 +x^ 2003 =0 are (where is a complex cube root of unity)
- If a,b,c are real numbers in G.P. such that a and c are positive, then the roots of the equation ax^2+bx+c=0
- The sum of non-real roots of the equation (x^2+x-2 ) (x^2+x-3 )=12, is
- The number of non-zero solutions of the equation x^2-5x- ( Sgn (x) )6=0, is
- The number of positive integral roots of x^4+x^3-4x^2+x+1=0 is
- If both the roots of the equation ax^2+bx+c=0 are zero, then
- If x^2+ax+10=0 and x^2+bx-10=0 have a common root, then a^2-b^2 is equal to
- The number of real roots of the equation (x+3)^4+(x+5)^4=16, is
- If (1+k) ^2x-4 x-1+k=0 has real roots x_1 and x_2, then
- If the roots of the equation x^2+a^2=8x+6a are real, then a belongs to the interval
- The equations ax^2+bx+a=0 and x^3-2x^2+2x-1=0 have 2 roots in common. Then a+b must be equal to