IPMAT WhatsApp Group
Sign in
Please select an account to continue using cracku.in
↓ →
IPMAT WhatsApp Group
The number of values $$a$$ can take such that $$x^4 + ax^3 + (3a - 4)x^2 + 2(a - 1)x - 4$$ can be expressed as a product of two quadratic polynomials, $$x^2 + px + 2$$ and $$x^2 + qx - 2$$, where $$p$$ and $$q$$ are real, is
Expand $$(x^2 + px + 2)(x^2 + qx - 2) = x^4 + (p+q)x^3 + pq \cdot x^2 + 2(q-p)x - 4$$.
Comparing with $$x^4 + ax^3 + (3a-4)x^2 + 2(a-1)x - 4$$:
Solving: $$q = \dfrac{2a-1}{2}$$, $$p = \dfrac{1}{2}$$. Substituting into $$pq = 3a-4$$: $$\dfrac{2a-1}{4} = 3a - 4 \Rightarrow a = \dfrac{3}{2}$$.
Only 1 value of $$a$$ works.
Create a FREE account and get:
Crack IPMAT 2026 with Cracku
Educational materials for IPMAT and IIMB UG preparation
Ask our AI anything
AI can make mistakes. Please verify important information.
AI can make mistakes. Please verify important information.
