All categories

3 years ago

Q(x)=x^3+ax^2+2b is divided by (x-3) and has a remainder of 4. Find the values of "a" and "b"

Mathematics

1 answer:

Sati [7]3 years ago

4 0

Answer:

Let p(x) = x3 + ax2 + bx +6

(x-2) is a factor of the polynomial x3 + ax2 + b x +6

p(2) = 0

p(2) = 23 + a.22 + b.2 +6 =8+4a+2b+6 =14+ 4a+ 2b = 0

7 +2 a +b = 0

b = - 7 -2a -(i)

x3 + ax2 + bx +6 when divided by (x-3) leaves remainder 3.

p(3) = 3

p(3) = 33 + a.32 + b.3 +6= 27+9a +3b +6 =33+9a+3b = 3

11+3a +b =1 => 3a+b =-10 => b= -10-3a -(ii)

Equating the value of b from (ii) and (i) , we have

(- 7 -2a) = (-10 - 3a)

a = -3

Substituting a = -3 in (i), we get

b = - 7 -2(-3) = -7 + 6 = -1

Thus the values of a and b are -3 and -1 respectively.

Step-by-step explanation:

You might be interested in

The diagonal of a rectangle is of length a. It splits each corner forming two angles with a ratio of 1:2. The area of the rectan

HACTEHA [7]

Answer:

Step-by-step explanation:

Given

Length of diagonal is a

Diagonal divides the angle in 1:2

such that $\theta +2\theta =90$ (because angle between two sides is 90)

$3\theta =90$

$\theta =30^{\circ}$

width of rectangle is $b=a\sin \theta =\frac{a}{2}$

Length of rectangle is $L=a\cos 30=\frac{\sqrt{3}}{2}a$

Area of rectangle $A=L\cdot b$

$A=\frac{\sqrt{3}}{2}a\times \frac{a}{2}$

$A=\frac{\sqrt{3}}{4}a^2$

5 0

3 years ago

The owner of a football team claims that the average attendance at games is over 523, and he is therefore justified in moving th

USPshnik [31]

Answer:

C) There is not sufficient evidence to support the claim that the mean attendance is greater than 523.

Step-by-step explanation:

Let μ be the the average attendance at games of the football team

The claim: the average attendance at games is over 523

Null and alternative hypotheses are:

$H_{0}$ : μ=523

$H_{a}$ : μ>523

The conclusion is failure to reject the null hypothesis.

This means that test statistic is lower than critical value. Therefore it is not significant, there is no significant evidence to accept the alternative hypothesis.

That is no significant evidence that the average attendance at games of the football team is greater than 523.

7 0

3 years ago

How do i draw 4 angles forming 4 linear pairs?

ser-zykov [4K]

Just do a line crossing another in a angle of 90°

1 is linear pair with 2, 2 is linear pair with 3, 3 is linear pair with 4 and 4 is linear pair with 1.

8 0

3 years ago

PLEASE HELP ME, ill give points! Im in the 7th grade

sdas [7]

Answer: y=-5 x=5

explanation: look at the number the x and y is on

4 0

2 years ago

Is it right And why

antiseptic1488 [7]

Yes it is indeed correct,
B. 7.47 is the correct answer!
Brainliest pls! thx! :)

7 0

3 years ago

Q(x)=x^3+ax^2+2b is divided by (x-3) and has a remainder of 4. Find the values of "a" and "b"​

Q(x)=x^3+ax^2+2b is divided by (x-3) and has a remainder of 4. Find the values of "a" and "b"