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3 years ago

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use the discriminant to determine how many and what kind of solutions the quadratic equation x²-x=-1/4 has

1 answer:

pantera1 [17]3 years ago

4 0

$\bf x^2-x=-\cfrac{1}{4}\implies \stackrel{\textit{multiplying by }\stackrel{LCD}{4}}{4x^2-4x=-1}\implies 4x^2-4x+1=0$

$\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{4}x^2\stackrel{\stackrel{b}{\downarrow }}{-4}x\stackrel{\stackrel{c}{\downarrow }}{+1} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} \boxed{0}&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-4)^2-4(4)(1)\implies 16-16\implies \boxed{0}$

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Vanyuwa [196]

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The coordinate ofthe deli is (1, -1)

Step-by-step explanation:

✍️Coordinate of Sally = (-3, 2)

Coordinate of Ocean Front = (5, -4)

The distance of Sally to Ocean Front Housing Complex = the distance between point (-3, 2) and (5, -4).

Use the distance formula, $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ , to calculate the distance between (-3, 2) and (5, -4):

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$d = \sqrt{(8)^2 + (-6)^2}$

$d = \sqrt{64 + 36}$

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✅The distance of Sally is 10 miles

✍️the coordinate of Deli would be half the distance between Sally and Ocean Front.

Therefore, use the midpoint formula to calculate the coordinate of the midpoint between Sally (-3, 2) and Ocean Front (5, -4).

Midpoint of (-3, 2) and (5, -4).

$M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$

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