Quadratic Equations
Product of Complex Expressions at Roots of Quartic
nta_pyq_2024_apr
Grade 11
Question:
Let $x_1,x_2,x_3,x_4$ be the solutions of the equation $4x^4+8x^3-17x^2-12x+9=0$ and $(4+x_1^2)(4+x_2^2)(4+x_3^2)(4+x_4^2)=\dfrac{125}{16}m$. Then the value of $m$ is
Step-by-Step Solution
Key Concept: Write $4x^4+8x^3-17x^2-12x+9=4(x-x_1)(x-x_2)(x-x_3)(x-x_4)$. Substitute $x=2i$ and $x=-2i$, then multiply the results.
$m=\frac{141^2+88^2}{125}=\frac{27625}{125}=221$.
Correct Answer: 221