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3 years ago

X^4-7x^2+9 (resolve into factors) Please help me I will mark you as brainliest.

Mathematics

1 answer:

SSSSS [86.1K]3 years ago

5 0

Factoring x4-7x2-9 

Factoring x4-7x2-9 The first term is, x4 its coefficient is 1 .

Factoring x4-7x2-9 The first term is, x4 its coefficient is 1 .The middle term is, -7x2 its coefficient is -7 .

Factoring x4-7x2-9 The first term is, x4 its coefficient is 1 .The middle term is, -7x2 its coefficient is -7 .The last term, "the constant", is -9 

Factoring x4-7x2-9 The first term is, x4 its coefficient is 1 .The middle term is, -7x2 its coefficient is -7 .The last term, "the constant", is -9 Step-1 : Multiply the coefficient of the first term by the constant 1 • -9 = -9 Step-2 : Find two factors of -9 whose sum equals the coefficient of the middle term, which is -7 .

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3 years ago

X^2+4x+y^2-10y+20=30 find the center of the circle by completing the square

swat32

Answer:

a). Center of the circle = (-2, 5)

b). Equation of the line ⇒ y = $-\frac{4}{5}x+\frac{58}{5}$

Step-by-step explanation:

Equation of the circle is,

x² + 4x + y²- 10y + 20 = 30

a). [x² + 2(2)x + 4 - 4] + [y²- 2(5)y + 25] - 25 + 20 = 30

[x² + 2(2)x + 4] - 4 + [y² - 2(5)y + 25] - 25 + 20 = 30

(x + 2)² + (y - 5)²- 29 + 20 = 30

(x + 2)² + (y - 5)²- 9 = 30

(x + 2)² + (y - 5)² = 39

By comparing this equation with the standard equation of a circle,

Center of the circle is (-2, 5).

b). A point (2, 10) lies on this circle.

Slope of the line joining this point to the center (-2, 5),

$m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

= $\frac{10-5}{2+2}$

= $\frac{5}{4}$

Let the slope of the tangent which is perpendicular to this line is ' $m_{2}$ '

Then by the property of perpendicular lines,

$m_{1}\times m_{2}=-1$

$\frac{5}{4}\times m_{2}=-1$

$m_{2}=-\frac{4}{5}$

Now the equation of the line passing though (2, 10) having slope $m_{2}=-\frac{4}{5}$

y - y' = $m_{2}(x-x')$

y - 10 = $-\frac{4}{5}(x-2)$

y - 10 = $-\frac{4}{5}x+\frac{8}{5}$

y = $-\frac{4}{5}x+\frac{8}{5}+10$

y = $-\frac{4}{5}x+\frac{58}{5}$

Therefore, equation of the line will be, y = $-\frac{4}{5}x+\frac{58}{5}$

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