Question

hi guys
plz answer and explain 7th and 8th Question
IX Maths
Related to ncert
UNNECESSARY answer will be DELETED
BEST answer will be mark as BRAINLIST ​

Answer 1

1)

Given -

• (x - 1) and (x + 3) are factors of x³ - ax² - 13x + b.

To Find -

• Value of a and b

As we know that :-

If (x - 1) and (x + 3) are factors of polynomial then x = 1 and x = -3 are its zeroes.

p(x) = x³ - ax² - 13x + b

Now,

p(1) = (1)³ - a(1)² - 13(1) + b = 0

→ 1 - a - 13 + b = 0

→ b - a = 12 ......... (i)

And

p(-3) = (-3)³ - a(-3)² - 13(-3) + b = 0

→ -27 - 9a + 39 + b = 0

→ b - 9a = -12 ......... (ii)

From (i) and (ii), we get :

b - a = 12

b - 9a = -12

(-) (+) (+)

__________

8a = 24

→ a = 3

Now, Substituting the value of a on (i), we get :

b - a = 12

→ b - 3 = 12

→ b = 15

Hence,

The value of a is 3 and b is 15

2)

Given -

• (x - 1) and (x + 2) are factors of 2x³ + ax² + bx - 14

To Find -

• Value of a and b

As we know that :-

If (x - 1) and (x + 2) are factors of polynomial then x = 1 and x = -2 are its zeroes.

p(x) = 2x³ + ax² + bx - 14

Now,

p(1) = 2(1)³ + a(1)² + b(1) - 14 = 0

→ 2 + a + b - 14 = 0

→ a + b = 12 ........ (i)

And

p(-2) = 2(-2)³ + a(-2)² + b(-2) - 14 = 0

→ -16 + 4a - 2b - 14 = 0

→ 4a - 2b = 30

→ 2(2a - b) = 30

→ 2a - b = 15 .......... (ii)

From (i) and (ii), we get :

a + b = 12

2a - b = 15

__________

3a = 27

→ a = 9

Now, Substituting the value of a on (i), we get :

a + b = 12

→ 9 + b = 12

→ b = 3

Hence,

The value of a is 9 and b is 3

Answer 2

$\huge \mathfrak{Answer:-}$

$\large\underline\mathrm{The \: value \: of \: a \: is \: 3 \: and \: b \: is \: 15 \: .}$

$\large\underline\mathrm{The \: value \: of \: a \: is \: 9 \: and \: b \: is \: 3.}$

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

(x - 1) and (x + 3) are factors of x³ - ax² - 13x + b.

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

• Value of a and b.

$\large\underline\mathrm{Solution}$

$\implies$ p(x) = x³ - ax² - 13x + b

$\implies$ (1)³ - a(1)² - 13(1) + b = 0

$\implies$ 1 - a - 13 + b = 0

$\implies$ b - a = 12. ...(1)

$\large\underline\mathrm{and}$

$\implies$ p(-3) = (-3)³ - a(-3)² - 13(-3) + b = 0

$\implies$ b - 9a = -12. ...(2)

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

$\implies$ b - c = 12

$\implies$ b - 9a = -12

_______________

$\implies$ 8a = 24

$\implies$ a = 3

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

$\large\underline\mathrm{putting \: the \: value \: of \: a \: on \: Eq. \: (1) \: .}$

$\implies$ b - a = 12

$\implies$ b - 3 = 12

$\implies$ b = 15

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

$\large\underline\mathrm{The \: value \: of \: a \: is \: 3 \: and \: b \: is \: 15 \: .}$

2$\large\underline\mathrm{Given:-}$

• (x - 1) and (x + 2) are factors of 2x³ + ax² + bx - 14

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

• Value of a and b

$\large\underline\mathrm{Solution}$

• p(x) => 2x³ + ax² + bx - 14

$\implies$ 2(1)³ + a(1)² + b(1) - 14

$\implies$ 2 + a + b - 14 = 0

$\implies$ a + b = 14. ...(1)

$\large\underline\mathrm{and}$

$\implies$ p(-2) => 2(-2)³ + a(-2)² + b(-2) - 14

$\implies$ -16 + 4a - 2b - 14 = 0

$\implies$ 4a - 2b = 30

$\implies$ 2(2a - b) = 30

$\implies$ 2a - b = 15. ...(2)

$\large\underline\mathrm{from \: Eq. \: (1) \: and \: Eq. \: (2) \: .}$

$\implies$ a + b = 12

$\implies$ 2a - b = 15

__________________

$\implies$ 3a = 27

$\implies$ a = 9

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

$\large\underline\mathrm{putting \: the \: value \: of \: a \: on \: Eq. \: (1).}$

$\implies$ a + b = 12

$\implies$ 9 + b = 12

$\implies$ b = 3.

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

$\large\underline\mathrm{The \: value \: of \: a \: is \: 9 \: and \: b \: is \: 3.}$

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