3 years ago

Which choice can be used to confirm that a quadrilateral is a parallelogram?

1 answer:

6 0

The answer would be <span>A quadrilateral is a parallelogram if it has one pair of sides that are both congruent and parallel.</span>

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The roots of 2x^{2} + 3x = 4 are α and β. Find the simplest quadratic equation which has roots <img src="https://tex.z-dn.net/?f

elena-s [515]

$2x^2+3x=4\implies2x^2+3x-4=0\implies x=\dfrac{-3\pm\sqrt{41}}4$

Let $\alpha$ be the root with the positive square root and $\beta$ the root with the negative square root. Then

$\dfrac1\alpha=\dfrac4{-3+\sqrt{41}}\quad\text{and}\quad\dfrac1\beta=\dfrac4{-3-\sqrt{41}}$

The simplest quadratic with these roots can be written as

$\left(x-\dfrac1\alpha\right)\left(x-\dfrac1\beta\right)=x^2-\left(\dfrac1\alpha+\dfrac1\beta\right)x+\dfrac1{\alpha\beta}=x^2-\dfrac34x-\dfrac12$