Answer:
a = 7 and b = - 18
Step-by-step explanation:
If (x - 1) is a factor of f(x) then x = 1 is a root and f(1) = 0, thus
f(1) = 1³ + 10(1)² + a + b = 0 and
1 + 10 + a + b = 0 ⇒ a + b = - 11 → (1)
Similarly if
(x + 2) is a factor then x = - 2 is a root and f(- 2) = 0
f(- 2) = (- 2)³ + 10(- 2)² - 2a + b = 0, thus
- 8 + 40 - 2a + b = 0 ⇒ - 2a + b = - 32 → (2)
Solve (1) and (2) simultaneously
Subtract (1) from (2)
- 3a = - 21 ( divide both sides by 3)
a = 7
Substitute a = 7 in (1)
7 + b = - 11 ⇒ b = - 11 - 7 = - 18
The required polynomial is
f(x) = x³ + 10x² + 7x - 18
<span>x^2 + y^2 + 8x – 6y + 21 = 0
x^2 + 8x +16 + y^2 -6y +9 = -21 + 16 +9
(x+4)^2 + (y-3)^2 = 4
So the radius is 2
</span>
Answer: -5
Step-by-step explanation:Absolute value is +5*-=-5
Answer:
the coefficient Is the number multiplied by a variable
The slope-intercept form:
y = mx + b
m - slope
b - y-intercept
We have y = 2x - 10. It's the slope-intercept form!
slope = 2
y-intercept = -10