Question

Let ∆ = $\left| \begin{matrix} x^{2} + 4x + 5 & x + 2 & 5 \\ 2x^{2} + 6x + 10 & 2x + 3 & 10 \\ 4x^{2}–2x + 20 & 4x–1 & 20 \end{matrix} \right|$, then

• A. y = ∆ represents a parabola passing through the origin
• B. y = ∆ represents a straight line through the origin
• C. ∆ = 0 has only one real root
• D. ∆ = 0 has two distinct real roots

Answer 1

Answer: (B)

y = ∆ represents a straight line through the origin

Answer 2

R₂ → R₂ – 2R₁

R₃ → R₃ – 4R₁

∆= $\left| \begin{matrix} x^{2} + 4x + 5 & x + 2 & 5 \\ –2x & –1 & 0 \\ –18x & –9 & 0 \end{matrix} \right|$

∆ = 5(18x – 18x)

∆ = 0

So y = ∆ = 0

y = 0 is a line passing through origin.