Question

1. List out the major reasons for why the middle class people turned against the aristocracy.
2. How did the New conservatism emerge after 1815?

answer quick very urgent

Answer 1

Answer:

Question

Question

Q. Given that the zeros of the cubic polynomial x³-6x²+3x+10 are the form of a, a+b and a+2b for some real number a and b find the values of a and b as well as the zeros of the given polynomial.

Given :-

a, a+b and a+2b are roots of x³-6x²+3x+10

Required to find :-

value of a and b and zeros of polynomial

\huge \huge \bf {\: \pmb{Solution}}

Solution

Solution

given that a, a+b and a+2b are roots of x³-6x²+3x+10

we know that sum of roots = \frac{-cofficient~of~x²}{coffiecient ~of~x³ }

coffiecient of x³

−cofficient of x²

= a + 2b + a + a + b = \frac{-(-6)}{1}

1

−(−6)

= 3a + 3b = 6

= 3 ( a + b ) = 6

= a + b = \frac{6}{3}

3

6

= a + b = 2 --- ( 1 )

= b = 2 - a

we know that product of roots = \frac{-constant}{coffiecient ~of~x³ }

coffiecient of x³

−constant

( a + 2b )( a + b )a = \frac{-10}{1}

1

−10

a + b + b ) ( a + b ) 2 = \frac{-10}{1}

1

−10

substituting equation 1 here,

= ( 2 + b ) (2)a = -10

= ( 2 + b ) 2a = -10

= ( 4 - a )2a = -10

= 4a - a² = \frac{-10}{5}

5

−10

= a² - 4a + 5 = 0

by splitting the middle term

= a² - 5a + a - 5 = 0

= a ( a - 5 ) + 1 ( a - 5 ) = 0

= ( a + 1 ) ( a - 5 ) = 0

→ a + 1 = 0

• a = -1

→ a - 5 = 0

• a = 5

→ when a = -1

= a + b = 2

= -1 + b = 2

= b = 2 + 1

= b = 3

• a = -1 , b = 3

→ when a = 5

= a + b = 2

= 5 + b = 2

= b = 2 - 5

= b = -3

• a = 5 , b = -3

Now, zeros of the given polynomial.

→ a = -1 & b = 3

• a = -1

• a+b = (-1) + 3 = 2

• a+2b = (-1) + 2 ( 3 ) = -1 + 6 = 5

→ a = 5 & b = -3

• a = 5

• a + b = 5 + (- 3 )= 2

• a + 2b = 5 + 2(-3) = 5 + (-6 )= -1