In each of these questions, two equations (I) and (II) are given. You have to solve both equations and give the answer. I. $4x^2 - 16x + 16 = 0$ II. $10y^2 - 29y + 21 = 0$

If x > y
If x ≥ y
If x < y
If x ≤ y

Correct answer: If x > y

Solution

Equation I factors as $4(x-2)^2=0$, so $x=2$. Equation II factors as $(5y-7)(2y-3)=0$, giving $y=\frac{7}{5}$ or $\frac{3}{2}$. In either case, the larger value of $x$ is greater than the roots of $y$, so the correct comparison is $x>y$.

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