`x ^(2) +1` has no real zeroes. Why ?

Given that a x^(2)+b x+c has no real roots and a+b+c lt 0 then,

Find values of k for which (k +4) x^(2) + (k +1) x+1 has equal zeros.

Let a, b, c be real. If a x^(2)+b x+c=0 has two real roots alpha and beta such that alpha lt -1 and beta gt 1 , then 1+(c)/(a)+|(b)/(a)| is

For which values of 'a' and 'b' are the zeroes of q(x) = x^(3) + 2x^(2) + a also the zeroes of the polynomial p(x) = x^(5) -x^(4) - 4x^(3) + 3x^(2) +3x+ b ? Which zeroes of p(x) are not the zeroes of q(x) ?

Show that the equation 2(a^(2)+b^(2))x^(2)+2(a+b)x+1=0 has no real roots when a!=b .

What is the value of k if the equation x^(2) +4x +(k +2) = 0 has one root equal to zero .

Find values of p for which the quadratic polynomial 4x^(2) + px +3 has equal zeros .

Let a in R and f : R rarr R be given by f(x)=x^(5)-5x+a , then (a) f(x)=0 has three real roots if a gt 4 (b) f(x)=0 has only one real root if a gt 4 (c) f(x)=0 has three real roots if a lt -4 (d) f(x)=0 has three real roots if -4 lt a lt 4

Find the values of a and b for which zeros of q(x) = x^(3) + 2x^(2) +a are also the zero of p(x) = x^(5) - x^(4) - 4x^(3) + 3x^(2) + 3x +bp . Also, find zeros of p(x) which are not zeros of q(x) .