Practice questions
88551 published questions with worked solutions.
- If a,b are odd integers, then the roots of the equation 2ax^2+(2a+b)x+b=0, a 0 are
- If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, then a,b,c are in
- Given that ax^2+bx+c=0 has no real roots and a+b+c<0, then
- The expression y=ax^2+bx+c has always the same sign as c if
- The values of a' for which the roots of the equation x^2+x+a=0 are real and exceed a' are
- If b>a, then the equation (x-a)(x-b)-1=0 has
- If , are the roots of ax^2+c=bx, then the equation (a+cy)^2=b^2y in y has the roots
- If a,b,c are all positive and in H.P., then the roots of ax^2+2bx+c=0 are
- If c and d are roots of the equation (x-a)(x-b)-k=0, then a,b are roots of the equation
- If the equations x^2+px+q=0 and x^2+p'x+q'=0 have a common root, then it is equal to
- If , are the roots of ax^2+bx+c=0, the equation whose roots are 2+ , 2+ is
- If ax^2+bx-c is divisible by x^2+bx+c, then a' is a root of the equation
- If the roots of the equation ax^2-4x+a^2=0 are imaginary and the sum of the roots is equal to their product, then a=
- If , are the roots of x^2-3x+a=0, a R and <1< , then
- If and are the roots of x^2+px+1=0 and and are the roots of x^2+qx+1=0, then the value of ( - )( - )( + )( + ), is
- If , are the roots of equation ax^2+bx+c=0, then the value of the determinant vmatrix 1& ( - )& ( - )&1& & &1 vmatrix , is
- The graph of the function y=16x^2+8(a+5)x-7a-5 is strictly above the x-axis, then a' must satisfy the inequality
- The values of p for which the difference between the roots of the equation x^2+px+8=0 is 2, are
- Product of the real roots of the equation t^2x^2+|x|+9=0, (t 0)
- If the equation x^2+px+q=0 has roots u and v where p,q are non-zero constants. Then