If the equation `(a-5)x^(2) + 2(a-10) x+ a+10= 0` has roots of opposite signs then find the values of a.

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 a) (-oo, -2) b) (-oo, 0) c) (-1, 0) d) (0, 1)

If the equation 2x^(2) + (a+3)x + 8 = 0 has equal roots, then one of the values of a is

If the equation x^(2) - (2 + m) x + (m^(2) - 4m + 4) = 0 in x has equal roots, then the values of m are

If the equations x^(2) + ax+1=0 and x^(2)-x-a=0 have a real common root b, then the value of b is equal to

For a ne b, if the equation x ^(2) + ax + b =0 and x ^(2) + bx + a =0 have a common root, then the value of a + b equals to:

If the equation 4x^2- 5x + k = 0 has two equal solutions. Find the value of k.