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3 years ago

What is the discriminant of the polynomial below 2x2 + 5x - 8?

Mathematics

2 answers:

mihalych1998 [28]3 years ago

7 0

Answer:

The discriminant of the given polynomial is 89.

Step-by-step explanation:

The given polynomial is

$P(x)=2x^2+5x-8$ .... (1)

If a polynomial is defined as

$P(x)=ax^2+bx+c$ .... (2)

then the discriminant of the polynomial is

$D=b^2-4ac$

From (1) and (2), we get

$a=2,b=5,c=-8$

The discriminant of the given polynomial is

$D=(5)^2-4(2)(-8)$

$D=25+64$

$D=89$

Therefore the discriminant of the given polynomial is 89.

larisa [96]3 years ago

3 0

The discriminant is 89

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stealth61 [152]

Answer:

Step-x ≤ 3

Given

2(4 + 2x) ≥ 5x + 5 ← distribute parenthesis on left side

8 + 4x ≥ 5x + 5 ( subtract 4x from both sides )

8 ≥ x + 5 ( subtract 5 from both sides )

3 ≥ x , hence

x ≤ 3by-step explanation:

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3 years ago

The center of a circle lies on the line y = 4x + 1 and is tangent to the x-axis at (−3,0) . What is the equation of the circle i

Hunter-Best [27]

Answer:

$(x+3)^2+(y+11)^2=121$

Step-by-step explanation:

Consider a sketch of the problem as shown in the picture, where:

Blue line is given by y = 4x + 1.
Point B is the center of the circle.
Point A is (-3, 0).

Since the center of the circle lies on the line y = 4x +1 and is tangent to the x-axis at point A, then its radius BA is perpendicular to the x-axis. To find the coordinates of point B, we must replace x = -3 into the blue line equation: y = 4x(-3) + 1 = -11.

So, we know that the center of the circle is at B=(-3, -11). And furthermore, the radius BA is of length r=11.

Since the <em>general equation of the circle</em> of radius lenght r centered at (h, k) is given by

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