Question

8b and 8c salve















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Answer 1

Answer:

$\huge \frak{ \pink{ \underline{ \underline{ \blue{★Question}}}}}$

Q. Find the value of a so that

ⓐ x² - 3x + 5a is divisible by x-2

ⓑ x + 1 is a factor of x³ + 9x² + ax + 15

ⓒ x - a is a factor of x³ - a²x + x + 2

$\huge \frak{\blue{ \underline{ \underline{ \pink{★Answer}}}}}$

$\large \frak{ \underline{Solⁿ \: ⓐ :}}$

$\sf{x - 2 = 0}$

$\sf \: x = 2$

Now,

$\sf \: f(x) = x² - 3x + 5a$

$\sf{∴ f(2) = (2)² - 3(2) + 5a = 0}$

$\sf4 - 6 + 5a = 0$

$\sf - 2 + 5a = 0$

$\sf5a = 2$

${\pink{ \boxed{∴ a = \frac{2}{5} }}}$

$\large \frak{ \underline{Solⁿ \: ⓑ :}}$

$\sf{x + 1 = 0}$

$\sf{x= -1}$

Now,

$\sf g(x)= x³ + 9x² + ax + 15$

$\sf ∴ g(-1)= (-1)³ + 9(-1)² + a(-1) + 15 = 0$

$\sf -1 + 9 - 1a + 15 = 0$

$\sf 23 - 1a = 0$

$\sf - 1a = -23$

$\blue{ \boxed{ ∴ a = 23}}$

$\large \frak{ \underline{Solⁿ \:ⓒ :}}$

$\sf x - a = 0$

$\sf x = a$

Now,

$\sf \: p(x) = x³ - a²x + x + 2$

$\sf{∴ p(a) = (a)³ - a²(a) + a + 2 = 0 }$

$\sf a³ - a³ + a + 2 = 0$

$\sf a + 2 = 0$

$\large{\purple{ \boxed{a = -2}}}$

Hope it helps....

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