Show `x^5-2x^2+7`=0 has atleast two imaginary roots.

Let a, b and c be the three sides of a triangle, then prove that the equation b^2x^2+(b^2+c^2-a^2)x+c^2=0 has imaginary roots.

If a, b , c in R and 3b^(2)-8ac lt 0 , then the equation ax^(4)+bx^(3)+cx^(2)+5x-7=0 has a) all real roots b) all imaginary roots c)exactly two real and two imaginary roots d) none

If b_1. b_2=2(c_1+c_2) then at least one of the equation x^2+b_1x+c_1=0 and x^2+b_2x+c_2=0 has a) imaginary roots b) real roots c) purely imaginary roots d) none of these

Let f(x)=a_(5)x^(5)+a_(4)x^(4)+a_(3)x^(3)+a_(2)x^(2)+a_(1)x, "where" a_(i),s are real and f (x) = 0 has a positive root alpha_(0). Then f^(prime)(x)=0 has a positive root alpha_1 such that 0 < alpha_1 < alpha_0 f^(prime)(x)=0 has at least two real roots f^('')(x)=0 has at least one real root none of these

If x^2-(a-3)x+a =0 has at least one positive root,then

True or false The equation 2x^2+3x+1=0 has an irrational root.

Fill in the blanks: Roots of the equation x^2-x+c=0 are always imaginary if the value of C is_____

Show that (x+yw+zw^2)^2+(xw^2+y+zw)^2+(xw+yw^2+z)^2=0 ,where w is an cube (imaginary ) root of 1.

Let P(x)=x^2+b x+cw h e r eba n dc are integer. If P(x) is a factor of both x^4+6x^2+25a n d3x^4+4x^2+28 x+5,t h e n a. P(x)=0 has imaginary roots b. P(x)=0 has roots of opposite c. P(1)=4 d . P(1)=6

If a ,b in R ,a!=0 and the quadratic equation a x^2-b x+1=0 has imaginary roots, then (a+b+1) is a. positive b. negative c. zero d. Dependent on the sign of b