Practice questions
88551 published questions with worked solutions.
- If a and b are two distinct real roots of the polynomial f(x) such that a<b, then there exists a real number c lying between a...
- If b and c are odd integers, then the equation x^2+bx+c=0 has
- Let , , , be the roots of x^4+x^2+1=0. Then, the equation whose roots are ^2, ^2, ^2, ^2 is
- If x^2+px+q=0 is the quadratic equation whose roots are a-2 and b-2 where a,b are the roots of x^2-3x+1=0, then
- The roots of ax^2+2bx+c=0 and bx^2-2 ac ,x+b=0 are simultaneously real, then
- If , are the roots of the equation x^2+ ,x+ =0, then the values of and are
- If the equation x^3+ax^2+b=0, b 0 has a root of order 2, then
- If is a root of the quadratic equation x^2+6x-2=0, then another root is
- If , are roots of the equation 375x^2-25x-2=0 and S_n= ^n+ ^n, then _ n _ r=1 ^nS_r is equal to
- For the equation |x|^2+|x|-6=0
- If a and b are the non-zero distinct roots of x^2+ax+b=0, then the least value of x^2+ax+b is
- The roots of the equation _2 (x^2-4x+5 )=(x-2) are
- If a,b,c are positive real numbers, then the number of real roots of the equation ax^2+b|x|+c=0 is
- If the roots of the equation 1 x+a + 1 x+b = 1c are equal in magnitude but opposite in sign, then their product is
- If , and are the roots of x^3+8=0, then the equation whose roots are ^2, ^2 and ^2 is
- If the roots of the equation x^3+bx^2+3x-1=0 form a non-decreasing H.P., then
- If , and are the roots of x^2+qx+r=0, then + is
- If (x-1)^3 is a factor of x^4+ax^3+bx^2+cx-1, then the other factor is
- If 7^ _7 (x^2-4x+5 ) =x-1, x may have values
- If and are the roots of the equation x^2+px+q=0 with p 0, then