Question

please answer please it's urgent and I will mark them as brain list??and don't know answers like I don't know etc...it's my request please understand..
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Answer 1

Answer:

This is answer to your question

Step-by-step explanation:

I hope that this will helpful to you

Answer 2

Step-by-step explanation:

If x-2 = 0

Then, x = 2

therefore,

$f(x) = {x}^{3} + a {x}^{2} + bx - 30 \\ => f(2) = {(2)}^{3} + a {(2)}^{2} + b(2) - 30 \\ =>f(2) = 8 + 4a + 2b - 30 \\ => f(2) = 4a + 2b -22 \: \: \: ........(i)$

If x+3 = 0

Then, x = -3

therefore,

$f(x) = {x}^{3} + a {x}^{2} + bx - 30 \\ => f( - 3) = {( - 3)}^{3} + a {( - 3)}^{2} + b( - 3) - 30 \\ =>f( - 3) = - 27+ 9a - 3b - 30 \\ => f( - 3) = 9a - 3b -57\: \: \: ........(ii)$

Since, both (x-2) and (x+3) are the factors of , so both of their values will be equal to 0.

${x}^{3} + a {x}^{2} + bx - 30$

BTP,

$4a + 2b - 22 = 0 \\ => 4a + 2b = 22 \\ => 2(2a + b) = 22 \\ => 2a + b = 11 \\ = > b = 11 - 2a \: \: \: .......(i)$

$9a - 3b - 57 = 0 \\ = > 9a - 3b = 57 \\ = > 3(3a - b) = 57 \\ = > (3a - b) = 19 \\ = > - (b - 3a) = 19 \\ = > b - 3a = - 19 \\ = > b = 3a - 19 \: \: \: ........(ii)$

Since, both (x-2) and (x+3) are the factors of , so both of their values will be equal.

BTP,

$11 - 2a = 3a - 19 \\ = > 3a - 19 = 11 - 2a \\ = > 3a + 2a = 11 + 19 \\ = > 5a = 30 \\ = > a = 6$

If a = 6,

then, b = 11-2a

=>b = 11-2×6

=>b = 11-12

=>b = -1

So, a= 6 and b= -1