(X+b) (x+c) where b <0 & c<0, the equation turns into x^2+gx+k
What is true about g and k
G<0 K>0
G<0 K<0
G>0 K>0
G>0 K<0
Two triangles r the same height. The slope side of triangle A is double the slope of B. how do the lengths of these two triangles compare?
x^2 + (b+c) x + bc
b+c is - so g is -
b*c is plus so k is +
so
the top one
Thanks so much :)
You are welcome :)
To simplify the expression (x+b)(x+c) where b < 0 and c < 0, we can apply the FOIL method. This method involves multiplying the First terms, the Outer terms, the Inner terms, and the Last terms together.
First, let's expand the expression using the FOIL method:
(x+b)(x+c) = x(x) + x(c) + b(x) + b(c)
= x^2 + cx + bx + bc
= x^2 + (c+b)x + bc
Since b < 0 and c < 0, their sum, (c+b), will also be negative. So, we can rewrite the equation as:
x^2 + (c+b)x + bc = x^2 + gx + k
Comparing the two equations, we see that:
g = (c+b)
k = bc
Now, let's analyze the values of g and k, based on the given constraints:
1. If b < 0 and c < 0, then their sum (c+b) will be negative. Therefore, g < 0.
2. Similarly, since both b and c are negative, their product (bc) will be positive. Hence, k > 0.
So, the correct statement is: G < 0 and K > 0.
Moving on to the second question:
If the two triangles have the same height, but the slope side of triangle A is double the slope of triangle B, we can compare their lengths using the concept of similar triangles.
In similar triangles, corresponding sides are in proportion to each other. The ratio of any two corresponding sides is equal to the ratio of their slopes. Since the slope of triangle A is double the slope of triangle B, we can infer that the ratio of their corresponding side lengths is also 2:1.
Therefore, the lengths of the two triangles are in the ratio of 2:1.