What are the roots of the equation x^2+3x-18=0

1 answer:

8 0

First you open 2 parenthesis with x in each one:

(x )(x )=0

Then, you place the sign of the second term (the x term) in the first parenthesis.

(x+ )(x )=0

Next, you multiply the signs of the x term and the sign of the constant (the third term).
Since + × - = -, then you place a -.

(x+ )(x- )=0

You look at the constant (-18) and the second term (3). What two numbers multiplied give you -18 but subtracted (since the signs inside the parenthesis are opposite) give you 3? Those numbers are 6 and 3.
Since the result of the substraction need to be 3, you place the 6 with the + sign and the 3 with the negative sign (if you think of it, 6-3=3 but 3-6 = -3. That's the reason behind placing the numbers)

(x+6)(x-3)=0

Therefore,

x+6=0 or x-3=0

x=-6 or x=3

Your roots are -6 and 3.

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...

255=WL and you are told that W=L+2 so the equation becomes:

255=(L+2)L

255=L^2+2L

L^2+2L-255=0

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2 years ago

Find the values of sin2u, cos2u, and tan2u given the figure.

Vadim26 [7]

Givens

y = 2

x = 1

z(the hypotenuse) = √(2^2 + 1^2) = √5

Cos(u) = x value / hypotenuse = 1/√5

Sin(u) = y value / hypotenuse = 2/√5

Solve for sin2u

Sin(2u) = 2*sin(u)*cos(u)

Sin(2u) = 2( $\dfrac{1}{\dsqrt{5}} * \frac{2}{\dsqrt{5}} = \dfrac{2}{5}$ ) = 4/5

Solve for cos(2u)

cos(2u) = - sqrt(1 - sin^2(2u))

Cos(2u) = - sqrt(1 - (4/5)^2 )

Cos(2u) = -sqrt(1 - 16/25)

cos(2u) = -sqrt(9/25)

cos(2u) = -3/5

Solve for Tan(2u)

tan(2u) = sin(2u) / cos(2u) = 4/5// - 3/5 = - 0.8/0.6 = - 1.3333 = - 4/3

Notes

One: Notice that you would normally rationalize the denominator, but you don't have to in this case. The formulas are such that they perform the rationalizations themselves.

Two: Notice the sign on the cos(2u). The sin is plus even though the angle (2u) is in the second quadrant. The cos is different. It is about 126 degrees which would make it a negative root (9/25)

Three: If you are uncomfortable with the tan, you could do fractions.

$\text{tan(2u)} = \dfrac{\dfrac{4}{5}}{\dfrac{-3}{5} } =\dfrac{4}{5} *\dfrac{5}{-3} =\dfrac{4}{-3}$