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3 years ago

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Which statement about the equation 3x ^ 2 + 9x - 12 = 0 is true ? 1 . The product of the roots is -12 . 2 The product of the roo

ts is -4 . 3 The sum of the roots is 3 . The sum of the roots is -9 .

1 answer:

svetlana [45]3 years ago

5 0

Answer:

Option : The product of the roots is - 4

Step-by-step explanation:

$3x^2 + 9x - 12 = 0\\\\3x^2 + 12x - 3x - 12 = 0\\\\3x(x+4) -3(x+4) = 0\\\\(3x - 3) (x+ 4) = 0\\\\$

Therefore the roots are -4 and 1

The product of the roots are -4 x 1 = -4

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Answer:

Part 1) The radius of the circle is r=17 units

Part 2) The points (-15,14) and (-15,-16) lies on this circle

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The distance between the center of the circle and any point on the circle is equal to the radius of the circle

the formula to calculate the distance between two points is equal to

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we have

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substitute

$r=\sqrt{(7+1)^{2}+(8+7)^{2}}$

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step 2

Find out the y-coordinate of point (-15,y)

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$(x-h)^2+(y-k)^2=r^2$

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substitute the values

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$(x+7)^2+(y+1)^2=289$

Substitute the value of x=-15 in the equation

$(-15+7)^2+(y+1)^2=289$

$64+(y+1)^2=289$

$(y+1)^2=289-64$

$(y+1)^2=225$

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$(y+1)=(+/-)15$

$y=-1(+/-)15$

$y=-1(+)15=14$

$y=-1(-)15=-16$

therefore

we have two solutions

point (-15,14) and point (-15,-16)

see the attached figure to better understand the problem

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