Out of the two roots of `x^(2)+(1-2 lambda)x+(lambda^(2)-lambda-2)=0` one root is greater than 3 and the other root is less than 3 ,then the limits of `lambda` are

Out of the two roots of x^(2)-2 lambda x+lambda^(2)-1=0 one is greater than 4 and the other root is less than 4, then the limits of lambda are

The values of a for which one root of the equation, x^(2)+(2a+1)x+(a-2)=0 is greater than 1 and the other root less than zero, is

If both the roots of the equation x^(2)-9x+a=0 are positive and one is greater than 3 and other is less than 3, then all possible values of a is-

The value of lambda for which the equation 2x^(2)-2(2 lambda+1)x+lambda(lambda+1)=0 may have one root less than lambda and other root greater than lambda are given by

for what values of m, the equation 2x^(2) -2 ( 2m +1) x+ m ( m +1) = 0 m in R has (i) Both roots smallar than 2 ? (ii) Both roots greater than 2 ? (iii) Both roots lie in the interval (2,3) ? (iv) Exactly one root lie in the interval (2,3) ? (v) One root is smaller than 1, and the other root is greater than 1 ? (vi) One root is greater than 3 and the other root is smaller than 2 ? (vii) Roots alpha and beta are such that both 2 and 3 lie between alpha and beta ?

Find the values of the parameter a for which the roots of the quadratic equation x^(2)+2(a-1)x+a+5=0 are such that one root is greater than 3 and the other root is smaller than 1.

If the equation x^(2)+2(lambda+1)x+lambda^(2)+lambda+7=0 has only negative roots,then the least value of lambda equals

If x^(2)+x-1=0 and 2x^(2)-x+lambda=0 have a common root then

If one root is greater than 2 and the other root is less than 2 for the equation x^(2)-(k+1)x+(k^(2)+k-8)=0 , then the value of k lies between