Question

If the two roots of the equation, $(a-1)(x^{4}+x^{2}+1)+(a+1)(x^{2}+x+1)^{2}=0$ are real and distinct, then the set of all values of ‘a’ is :
(a) $\bigg \lgroup 0,\ \frac{1}{2}\bigg \rgroup$(b) $\bigg \lgroup -\frac{1}{2}, 0\bigg \rgroup \cup \bigg \lgroup0,\ \frac{1}{2}\bigg \rgroup$(c) $\bigg \lgroup -\frac{1}{2}, 0\bigg \rgroup$
(d) (–∞, –2) ∪ (2, ∞)

Answer 1

(a) $\bigg \lgroup 0,\ \frac{1}{2}\bigg \rgroup$(b) $\bigg \lgroup -\frac{1}{2}, 0\bigg \rgroup \cup \bigg \lgroup0,\ \frac{1}{2}\bigg \rgroup$(c) $\bigg \lgroup -\frac{1}{2}, 0\bigg \rgroup$

(d) (–∞, –2) ∪ (2, ∞)