Question

plz slove it ..i need to sumbit it

Answer 1

Answer :

3)

{ See the solution in the attachment }

We see that the remainder is

= - 22x + 5

Hence, we need to subtract ( - 22x + 5) from the given polynomial to get the required solution.

4)

The given polynomial is

f (x) = ax³ + x² - 2x + b

Since, (x - 1) is a factor of f (x),

a 1³ + 1² - 2 (1) + b = 0

or, a + 1 - 2 + b = 0

or, a + b = 1 ...(i)

Also, (x + 1) is a factor of f (x); so

a (- 1)³ + (- 1)² - 2 (- 1) + b = 0

or, - a + 1 + 2 + b = 0

or, a - b = 3 ...(ii)

Now, adding (i) and (ii), we get

a + b + a - b = 1 + 3

or, 2a = 4

or, a = 2

Putting a = 2 in (i), we get

2 + b = 1

or, b = 1 - 2

or, b = - 1

Hence, a = 2 and b = - 1

5)

Given that,

x + y = 12 and xy = 32

So, x² + y²

= (x + y)² - 2xy

= 12² - 2 (32)

= 144 - 64

= 80

6)

Given that,

3x + 2y = 12 and xy = 6

Now, 9x² + 4y²

= (3x + 2y)² - 2 (3x) (2y)

= 12² - 12xy

= 144 - 12 (6)

= 144 - 72

= 72

7)

Given that,

x - $\frac{1}{x}$ = 4

Now,

$(x + \frac{1}{x})^{2}$

= $(x -\frac{1}{x})^{2} + 2 (x) (\frac{1}{x})$

= 4² + 2

= 16 + 2

= 18

Then, x + $\frac{1}{x} = \sqrt{18}$

= 3 $\sqrt{2}$

Hence,

$x^{2} - \frac{1}{x^{2}}$

= $(x + \frac{1}{x})(x - \frac{1}{x})$

= 4 × 3$\sqrt{2}$

= 12 $\sqrt{2}$

#MarkAsBrainliest