It looks like you might have intended to say the roots are 7 + i and 5 - i, judging by the extra space between 7 and i.
The simplest polynomial with these characteristics would be
but seeing as each of the options appears to be a quartic polynomial, I suspect f(x) is also supposed to have only real coefficients. In that case, we need to pair up any complex root with its conjugate to "complete" f(x). We end up with
which appears to most closely resemble the third option. Upon expanding, we see f(x) does indeed have real coefficients:
2(4)2 - 10 / 2 = 8(2) - 10 / 2 = 16 - 5 = 11 (FINAL ANSWER)
The given pentagon can be divided into two figures : a triangle and rectangle as shown in figure.
Let us find area of each figure separately.
Triangle:
Area of triangle is given by:
where b=base and h=height
Height of triangle :
h=(3x+5)-(2x+1)
h=x+4
Base = 2x-2
Area of triangle= (x-1)(x+4) = x²+3x-4
Area of rectangle:
Area of rectangle is given by:
A=l*b
Area of rectangle = 4x²-2x-2
Area of pentagon = Area of triangle + Area of rectangle
Area of pentagon = x²+3x-4 + 4x²-2x-2
Area of pentagon = 5x²+x-6
If area of pentagon is 42 cm², then solving for x,
Factorising to get x,
x=-3.2 and x=3
If we take x as negative the side will be negative, so we neglect x=-3.2
So x=3 is the answer.
Answer:
A
Step-by-step explanation:
i think
