Question

pls answer this with explanation ​

Answer 1

Step-by-step explanation:

Given -

(x + 2) and (x - 1) are factors of (x³ + 10x² + mx + n)

To Find -

Value of m and n

Now,

If (x + 2) and (x - 1) are factors of (x³ + 10x² + mx + n)

Then,

Zeroes are -

• x = -2 and x = 1

Now,

Substituting the value of x = -2 on (x³ + 10x² + mx + n), we get :

» (-2)³ + 10(-2)² + m(-2) + n = 0

» -8 + 40 - 2m + n = 0

• » 2m - n = 32 ............ (i)

And

Substituting the value of x = 1 on

(x³ + 10x² + mx + n), we get :

» (1)³ + 10(1)² + m(1) + n = 0

» 1 + 10 + m + n = 0

• » m + n = -11 ............. (ii)

Now,

Solving equation (i) and (ii), we get :

» 2m - n = 32

m + n = -11

_____________

» 3m = 21

• » m = 7

And

Substituting the value of m on equation (ii), we get :

» m + n = -11

» 7 + n = -11

» n = -11 - 7

• » n = -18

Hence,

The value of m is 7 and n is -18

Answer 2

$\huge \mathfrak{Answer:-}$

$\implies$ m = 7

$\implies$ n = -18

$\large\underline\mathrm{Given:-}$

• (x + 2) and (x - 1) and factors of (x³ + 10x² + Mx + n)

$\large\underline\mathrm{To \: find}$

• value of m and m
• x = -2
• x = 1

$\large\underline\mathrm{Solution}$

• put the value of x = -2

$\implies$ x³ + 10x² + mx + n

$\implies$ (-2)³ + 10(-2)² + m(-2) + n

$\implies$ -8 + 40 - 2m + n = 0

$\implies$ 2m - n = 32______(1)

$\large\underline\mathrm{And}$

• put the value of x = 1

$\implies$ x³ + 10x² + mx + n

$\implies$ (1)³ + 10(1)² + m(1) + n

$\implies$ 1 + 10 + m + n = 0

$\implies$ m + n = -11______(2)

$\large\underline\mathrm{Now,}$

$\large\underline\mathrm{equation \: (1) \: and \: (2) \; , \: we \: get.}$

2m - n = 32

m + n = -11

-----------------

3m = 21

$\implies$ m = 7

$\large\underline\mathrm{The \: value \: of \: m \: on \: equation \: (2)}$

$\implies$ m + n = -11

$\implies$ 7 + n = -11

$\implies$ n = -11 - 7

$\implies$ n = -18

$\large\underline\mathrm{Hence,}$

$\large\underline\mathrm{The \:value \: of \: m \: is \: 7 \: and \: n \: is \: -18}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$