Question

if ( X+1) is a factor of 2x cube +ax square + 2 bx+1 then find the value of a and b given that 2a-3b= 4
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Answer 1

➙ Given that (x+1) is a factor of p(x)

➙ Therefore, -1 is a zero of given p(x)

• herefore, -1 is a zero of given p(x) p(x) = 2x³ + ax² + 2bx + 1

➙ Substituting the value of -1 in the given p(x),we get

➡ p(x)=2(-1)³ + a(-1)² + 2b(-1) + 1

➡ -2 + a -2b + 1

➡ -1 + a - 2b

➡ a - 2b = 1

• Also given that 2a - 3b = 4

• So we got two equations

↪ a - 2b = 7 ...(1)

↪ 2a - 3b = 4 ...(2)

➡ (1)* (2)* (4)- 2 = 2a - 4b = (3)

➡ (2)* 1 = 2a - 3b = 4 (4)

➡ (4) - (3) = [2a - 2a ] + [-3b - (-4b)] = 4 - 2

➡ -3b + 4b = 2

∴ b = 2

• Substituting the value of b in (3)

➡ 2a - 4b = 2

➡ 2a - (4*2) = 2

➡ 2a - 8 = 2

➡ 2a = 2 + 8

➡ 2 = 10

➡ a = 10 / 2

∴ a = 5

Hence, a = 5 & b = 2

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Step-by-step explanation:

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Answer 2

➙ Given that (x+1) is a factor of p(x)

➙ Therefore, -1 is a zero of given p(x)

therefore, -1 is a zero of given p(x) p(x) = 2x³ + ax² + 2bx + 1

➙ Substituting the value of -1 in the given p(x),we get

➡ p(x)=2(-1)³ + a(-1)² + 2b(-1) + 1

➡ -2 + a -2b + 1

➡ -1 + a - 2b

➡ a - 2b = 1

Also given that 2a - 3b = 4

So we got two equations

↪ a - 2b = 7 ...(1)

↪ 2a - 3b = 4 ...(2)

➡ (1)* (2)* (4)- 2 = 2a - 4b = (3)

➡ (2)* 1 = 2a - 3b = 4 (4)

➡ (4) - (3) = [2a - 2a ] + [-3b - (-4b)] = 4 - 2

➡ -3b + 4b = 2

∴ b = 2

Substituting the value of b in (3)

➡ 2a - 4b = 2

➡ 2a - (4*2) = 2

➡ 2a - 8 = 2

➡ 2a = 2 + 8

➡ 2 = 10

➡ a = 10 / 2

∴ a = 5

Hence, a = 5 & b = 2

☛ ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ʏᴏᴜ.