We are given the quadratic equation :
Now let us use AC method to factorise it.
Step 1:
Find product of A and C
A=1 and C =-32
A*C =-32
Step 2:
Find factors of -32 such that they add up to give -14.
Factors of -32 that add up to give -14 are -16 and 2.
Step 3:
Rewrite the equation using factors found in step 2.
Step 4:
Factoring by grouping.
Step 5:
Find roots.
x-16=0 gives x=16
x+2=0 gives x=-2
Answer : Roots of the given Polynomial equation are 16 and -2.
Answer:
Step-by-step explanation:
The x-intercepts are the points with y- coordinate of 0
- (x - 3)(x + 8) = 0
- x - 3 = 0 or x + 8 = 0
- x = 3 or x = - 8
a) x-intercepts are
b) midpoint of x-intercepts is
- (3 - 8)/2 = - 5/2 = - 2.5
c) The extheme value has x- coordinate of - 2.5 and y- coordinate
- (-2.5 - 3)(- 2.5 + 8) = (-5.5)(5.5) = - 30.25
d) f(- 2.5) = - 30.25
Answer:
a) P = (-3, 4, 3)
b) P = (7, 4, 1)
Step-by-step explanation:
a) You want Q-P = (5, 4, -1) where Q = (2, 0, 2). Solving for P, we get ...
P = Q - (5, 4, -1) = (2-5, 4-0, 2-(-1))
P = (-3, 4, 3)
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b) The vector in the opposite direction of the one given is the given one multiplied by -1.
P = Q - (-1)(5, 4, -1) = (2+5, 0+4, 2-1)
P = (7, 4, 1)
Look at the gradient of both the equations (the x multiplier, usually known as m), and there are a couple of rules:
Parallel: The gradients are identical
Perpendicular: Look at the gradients as fractions. To get the perpendicular to a gradient you flip the fraction and change the sign. If this is the case for the two gradients, then they are perpendicular.
