<span>The general form of quadratic equation with real
coefficients and leading coefficient 1, has x = -bi as a root
=> x = <u>-b + </u></span><u>√ b^2 – 4 ac</u><span>
2a
It is also written as:
=> ax^2 + bx + c = 0
Quadratic equation involves unknown numbers which is x, the numbers which a, b
and c are called coeffecients.
There are also quadratic factorization where you factor the polynomial give to
be able to get the value of the equation.</span>
Answer:
k = -18
Step-by-step explanation:
If x-3 is a factor, what this means is that if we substitute;
x = 3 into the equation, we should get 0
This is from the factor theorem
Thus ;
P(3) = 0 = 2(3)^3 -5(3)^2 + 3(3) + k
0 = 54 - 45 + 9 + k
k + 18 = 0
k = -18
Answer:
Step-by-step explanation:
The straight line passes through (0,1) and (2,-2).
Equation of a straight line passing through two points (x1,y1) and (x2,y2)
is given by:
Everything to the left of the line is shaded.
We have to visualize the graph:the straight line has a positive y-intercept and a negative slope.The graph is given in the attachment below.
From the figure we can see origin lies on the shaded region.Hence (0,0) should satisfy the inequality.
LHS=y=0
RHS=
LHS<RHS as 0<1
Hence , the inequality is:
Use Pythagorean Theorem:
a² + b² = c²
"a" is one side of the right triangle.
Its length is: radius of larger circle minus radius of smaller circle: (11 - 3 = 8)
The distance between the center of the circles creates the hypotenuse (17)
8² + b² = 17²
b² = 225
b = 15
Answer: the length of the common external tangent is 15.
