Practice questions
88551 published questions with worked solutions.
- The value of p for which both the roots of the equation 4x^2-20px+ (25p^2+15p-66 )=0 are less than 2, lies in
- Let x_1,x_2 be the roots of the equation x^2-3x+p=0 and let x_3,x_4 be the roots of the equation x^2-12x+q=0. If the numbers...
- If the roots of ax^2-bx-c=0 change by the same quantity, then the expression in a,b,c that does not change is
- If the sum of the roots of the equation (a+1)x^2+(2a+3)x+(3a+4)=0 is -1, then the product of the roots is
- If one root of the equation 5x^2+13x+k=0 is reciprocal of other, then the value of k is
- If the expressions x^2-11x+a and x^2-14x+2a have a common root, then the values of a' is
- If the equations ax^2+bx+c=0 and 2x^2+3x+4=0 have a common root, then a:b:c
- The number of real roots of the equation (x-1)^2+(x-2)^2+(x-3)^2=0 is
- If m Z and the equation mx^2+(2m-1)x+(m-2)=0 has rational roots, then m is of the form
- If the equation x^3-3x+a=0 has distinct roots between 0 and 1, then the value of a is
- If roots of ax^2+bx+c=0, a,b,c R, a 0 are imaginary then
- Let S denote the set of all real values of a for which the roots of the equation x^2-2ax+a^2-1=0 lie between 5 and 10, then S...
- The set of values of a' for which x^2+ax+ ^ -1 (x^2-4x+5 )+ ^ -1 (x^2-4x+5 )=0 has at least one real root is given by
- If the equation 2x^2-7x+1=0 and ax^2+bx+2=0 have a common root, then
- The equation (x-b)(x-c)+(x-a)(x-b)+(x-a)(x-c)=0 has all its roots
- If a+b+c=0 and a c then the roots of the equation (b+c-a)x^2+(c+a-b)x+(a+b-c)=0, are
- The number of real roots of the equation |x|^2-3|x|+2=0 is
- If x+1 is a factor of x^4+(p-3)x^3-(3p-5)x^2+(2p-9)x+6, then p is
- If is a root of 25x^2+5x-12=0, -1<x<0. Then the value of 2 is
- If , are the roots of the equation x^2+px+q=0 and ^4, ^4 are the roots of x^2-rx+s=0, then the equation x^2-4qx+2q^2-r=0 has...