turkey-yks 2024 Q19

turkey-yks · Other · yks-ayt Discriminant and conditions for roots Condition for repeated (equal/double) roots

Let $a$ and $b$ be real numbers. In the rectangular coordinate plane, the parabola $y = x^{2} + ax + b$ is tangent to the $x$-axis and to the line $y = x$.
What is the product $a \cdot b$?
A) $\dfrac{1}{2}$ B) $\dfrac{1}{4}$ C) $\dfrac{1}{8}$ D) $\dfrac{1}{16}$ E) $\dfrac{1}{32}$

Let $a$ and $b$ be real numbers. In the rectangular coordinate plane, the parabola $y = x^{2} + ax + b$ is tangent to the $x$-axis and to the line $y = x$.

What is the product $a \cdot b$?

A) $\dfrac{1}{2}$
B) $\dfrac{1}{4}$
C) $\dfrac{1}{8}$
D) $\dfrac{1}{16}$
E) $\dfrac{1}{32}$

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