Question

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Answer 1

Solution :

Case 1)

• p(x) = 2x³ + x² - ax + 2

• g(x) = (x-2)

When g(x) = 0

→ g(x) = 0

→ x - 2 = 0

→ x = 0 + 2

→ x = 2

Put the value of x = 2 in p(x)

→ p(2) = 2(2)³ + (2)² - a(2)+ 2

→ p(2) = 2(8) + 4 - 2a + 2

→ p(2) = 16 + 4 - 2a + 2

→ p(2) = -2a + 22....(i)

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Case 2)

• p(x) = 2x³ - 3x² -3x + a

• g(x) = x - 2

When g(x) = 0

→ g(x) = 0

→ x - 2 = 0

→ x = 0 + 2

→ x = 2

Put the value of x = 2 in p(x)

→ p(2) = 2(2)³ - 3(2)² -3(2)+ a

→ p(2) = 2(8) - 3(4) - 6 + a

→ p(2) = 16 - 12 - 6 + a

→ p(2) = 4 - 6 + a

→ p(2) = a - 2....(ii)

According to the Question :

→ -2a + 22 = a - 2

→ -2a - a = -2 - 22

→ -3a = -24

→ a = $\sf\cancel\dfrac{-24}{-3}$

→ a = 8

$\therefore$ The value of a = 8

Answer 2

Answer:

$\huge\boxed{\pink{\underline{\sf{Answer=8}}}}$

Please check attachments for explanation.