Answer:
The polynomial with real coefficients having zeros 2 and 2 - 2i is
x³ - 6x² + 16x - 16 = 0
Step-by-step explanation:
Given that a polynomial has zeros at 2 and 2 - 2i, we want to write this polynomial.
We have
x - 2 = 0
x - (2 - 2i) = 0
=> x - 2 + 2i = 0
Since the polynomial has real coefficients, and 2 - 2i is a zero of the polynomial, the conjugate of 2 - 2i, which is 2 + 2i is also a polynomial.
x - (2 + 2i) = 0
=> x - 2 - 2i = 0
Now,
P(x) = (x - 2)(x - 2 + 2i)(x - 2 - 2i) = 0
= (x - 2)((x - 2)² - (2i)²) = 0
= (x - 2)(x² - 4x + 8) = 0
= x³ - 4x² + 8x - 2x² + 8x - 16 = 0
= x³ - 6x² + 16x - 16 = 0
This is the polynomial required.
Answer:
22 1/2
Step-by-step explanation:
Answer:
a) f(6)=(6)^2+4(6)+1=65
b)f (x+9)=(x+9)^2+4 (x+9)+1=(x^2+18x+81)+(4x+36)+1=x^2+22x+117
f (-x)=(-x)^2-4x+1
Answer:
25? to be honest i really dont know :/
Step-by-step explanation:
um pemdas says 5x5 is 25 so 5+(25)-5/5 then you do -5/5 is -1 and thats 5+(25)-5 then you add 5 to 25 and thats 30 and minus 5 is 25
let, x be the no of coins then according to question.Mary have 3x no of coins and John have x no of coins..
now, 3x+x=180
or,4x=180
or,x=180/4
therefore, x= 45
thus mary has 3×45=135 no of coins...