Math, asked by nishchay8b21, 12 days ago

Attachments:

1

Step-by-step explanation:

1st Q :- put q(x) = 0

x+2 = 0

x = -2

Now put x = -2 in p(x)

4(-2)^4 + 2(-2)^3 -3 (-2)^2 + 8(-2) + 5a

64 - 16 - 12 - 16 + 5a = 0

20 + 5a = 0

a = -20/5 = -4

2nd Q :-    625 = 5^4

Mean of observations = SUM / TOTAL NUMBER = x^4 - 5^4 / x+5 = x^3 - 5^3 = x^3 - 125

3rd Q:- Let the radius be x

area of circle = pie r^2

Pie x^2 = piex^2 + 6x pie + 9 pie

pie x^2 = pie x ^2 + 3x pie + 3x pie + 9 pie (BY MID TERM SPLITTING)

pie x^2 = pie x (x +3) + 3 pie (x + 3)

pie x^2 = (pie x + 3 pie) (x+3)

x^2 = pie (x+3) (x+3) / pie

x^2 = (x+3)^2

Therefore x = x+3

:D

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Thank you..

2

Question given :

a ) Find the value of a , if x + 2 is a factor of the polynomial 4x⁴ + 2x³ - 3x² + 8x + 5a

b ) The sum of x + 5 observations is x⁴ - 625 . Find the mean of the observations

c ) The area of a circle is given by the expression πx² + 6xπ + 9π Find the radius of the circle

Required solution:

Answer 1 : If x + 2 is a factor of 4x⁴ + 2x³ - 3x² + 8x + 5a then ,

• x + 2 = 0
• x = - 2

Substitute the value of x in the following polynomial ,

• p(x) = 4x⁴ + 2x³ - 3x² + 8x + 5a

• p(-2) = 4(-2)⁴ + 2(-2)³ - 3(-2)² + 8(-2) + 5a

• 4(16) + 2(-8) - 3(4) + 8(-2) + 5a = 0

• 64 - 16 - 12 - 16 + 5a = 0

• 20 + 5a = 0

• 5a = 20

• a =

• a = 4

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer 2 : We know that mean is equal to the sum of observations over total observations . So ,

• Mean =

• Mean =

• Mean =

• Mean =

• Mean = x³ - 125

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer 3 : Let the radius be x in the given case . We know that the area of the circle is given by the expression πx² + 6xπ + 9π. So

• Area = πx²

• πx² + 6xπ + 9π = πx²

• π ( x² + 6x + 9 ) = πx²

• π × ( x + 3 )² = πx²

• ( x + 3 )² =

• ( x + 3 )² = x²

• x = x + 3

Therefore the radius is x + 3

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