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2 years ago

9

Write the quadratic equation whose roots are six and -2 and who’s leading coefficient is 3 use the letter X to represent the var

iable

1 answer:

Artist 52 [7]2 years ago

6 0

Answer:

$3X^{2} - 12X - 36 = 0$

Step-by-step explanation:

6 and - 2 are the only two solutions to the required quadratic equation.

So, if the variable is represented by X then (X - 6) and (X + 2) will be the only two factors of the polynomial function.

Therefore, the equation is

(X - 6)(X + 2) = 0

⇒ $X^{2} - 4X - 12 = 0$

If the leading coefficient of the equation is 3 then we can write the equation as $3X^{2} - 12X - 36 = 0$ (Answer)

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Tan2x = 3
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2 years ago

Match each pair of points to the equation of the line that is parallel to the line passing through the points.

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we know that

If two lines are parallel, then, their slopes are equal.

The formula to calculate the slope between two points is equal to

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<u>Case A)</u> Point $B(5,2)\ C(7,-5)$

Find the slope BC

Substitute the values in the formula

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so

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therefore

<u>the answer Part A) is</u>

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<u>Case B)</u> Point $D(11,6)\ E(5,9)$

Find the slope DE

Substitute the values in the formula

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so

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therefore

<u>the answer Part B) is</u>

$D(11,6)\ E(5,9)$ ------> $y=-0.5x-3$

<u>Case C)</u> Point $F(-7,12)\ G(3,-8)$

Find the slope FG

Substitute the values in the formula

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Any linear equation with slope $m=-2$ will be parallel to the line passing through the points $F(-7,12)\ G(3,-8)$

<u>Case D)</u> Point $H(4,4)\ I(8,9)$

Find the slope HI

Substitute the values in the formula

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$m=\frac{5}{4}$

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therefore

<u>the answer Part D) is</u>

$H(4,4)\ I(8,9)$ ------> $y=1.25x+4$

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Find the slope JK

Substitute the values in the formula

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so

Any linear equation with slope $m=-0.375$ will be parallel to the line passing through the points $J(7,2)\ K(-9,8)$

<u>Case F)</u> Point $L(5,-7)\ M(4,-12)$

Find the slope LM

Substitute the values in the formula

$m=\frac{-12+7}{4-5}$

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The equation $y=5x+19$ is parallel to the line passing through the points $L(5,-7)\ M(4,-12)$

therefore

<u>the answer Part F) is</u>

$L(5,-7)\ M(4,-12)$ ------> $y=5x+19$

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