Answer: A=2 and B=13
Explanation: The Factor Theorem states that if a is the root of any polynomial p(x) that is if p(a)=0, then (x−a) is the factor of the polynomial p(x).
Let p(x)=x
3
+ax
2
−bx+10 and g(x)=x
2
−3x+2
Factorise g(x)=x
2
−3x+2:
x
2
−3x+2=x
2
−2x−x+2=x(x−2)−1(x−2)=(x−2)(x−1)
Therefore, g(x)=(x−2)(x−1)
It is given that p(x) is divisible by g(x), therefore, by factor theorem p(2)=0 and p(1)=0. Let us first find p(2) and p(1) as follows:
p(1)=1
3
+(a×1
2
)−(b×1)+10=1+(a×1)−b+10=a−b+11
p(2)=2
3
+(a×2
2
)−(b×2)+10=8+(a×4)−2b+10=4a−2b+18
Now equate p(2)=0 and p(1)=0 as shown below:
a−b+11=0
⇒a−b=−11.......(1)
4a−2b+18=0
⇒2(2a−b+9)=0
⇒2a−b+9=0
⇒2a−b=−9.......(2)
Now subtract equation 1 from equation 2:
(2a−a)+(−b+b)=(−9+11)
⇒a=2
Substitute a=2 in equation 1:
2−b=−11
⇒−b=−11−2
⇒−b=−13
⇒b=13
Hence, a=2 and b=13.
Try to follow the steps im giving you here and you will get to the answer:
<span>y = x^2-8x+12
put x=4
y= 4^2 - 8(4) +12
y= 16 - 32 +12
y = -4
</span>I hope this is what you need :)
Answer:
B. The statement is false because -5 is to the left of -3 on a number line.
Step-by-step explanation:
Statement: -5 > -3
A number line system is a method of locating and expressing the position of directed numbers. It has its middle mark as zero, so that all numbers to the left of zero are less than zero and all numbers to the right of zero are greater than zero.
Comparing two directed numbers -5 and -3. It can be observed that -3 is greater than -5, so that -5 is to the left of -3 on a number line.
Thus -5 > -3 is false.
<span>Label the place value 12 354.897
=> the given numbers are mixed number. We have the whole number which is 12
354 and the decimals which id 897.
Now, Let us label each digit’s place values:
1 – ten thousands = equals to 10 000
2 – thousands = equals to 2 000
3 – hundreds = equals to 300
5 – tens = equals to 50
4 – ones = equals to 4
.8 – tenths = equals to 8/10
.09 – hundreds = equals to 9/100
.007 – thousands = equals to 7/1 000</span>