Find the interval for a for which `3x^2 +2(a^2 +1)x+(a^2 - 3a +2)` possesses roots of opposite sign.

Find all real value of a for which the equation x^4 + (a - 1)x^3+ x^2 + (a - 1)x + 1 = 0 possesses at least two distinct positive roots

If the equation (a-5)x^2+2(a-10)x+a+10=0 has roots of opposite sign, then find the value of adot

Find the intervals in which the function f given by f(x) = 2x^(3) – 3x^(2) – 36x + 7 is (a) increasing (b) decreasing

Find the other root of x^(2) - 4x + 1 = 0 given that 2 + sqrt3 is a root:

The equation 2^(2x) + (a - 1)2^(x+1) + a = 0 has roots of opposite sing, then exhaustive set of values of a is

If the roots of the quadratic equation 3x^(2)+2x+a^(2)-a=0 in x are of opposite signs, then a lies in the interval

The range of a for which the equation x^2+ax−2=0 has its smaller root in the interval (−1,-3) is

If x = -2 is one root of x^(3) - x^(2) - 17x = 22 . Then find the other roots of the equation.

If x=-2 is one root of x^3 -x^2 -17x =22 then find the other roots of the equation.

Find the values of x for which matrix [(3,-1+x,2),(3,-1,x+2),(x+3,-1,2)] is singular.