Let `A={a in R}` the equation `(1+2i)x^3-2(3+i)x^2+(5-4i)x+a^2=0` has at least one real root. Then the value of `(suma^2)/2` is_______.

If (x^(2) + 5)/(2) = x - 2 cos (m + nx) has at least one real root, the

Without actually solving show that the equation x^(4)+2x^(3)-2=0 has only one real root in the interval (0,1) .

If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value of (a^2)/(b^2) is_______

Find the condition if the equation 3x^2+4a x+b=0 has at least one root in (0,1)dot

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 b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one real root.

Show that 3x^9-10x^5+3x^4+2x^2+7=0 has at least 6 imaginary roots.

The values of 'a' for which the equation (x^2 + x + 2)^2 - ( a-3)( x^2+ x+2)(x^2 +x + 1) + (a-4)(x^2 + x + 1)^2 = 0 has atlesast one real root is: