Question

if 0and 1 are the zeros of the polynomial f(x) 2x cube +3x square +ab+b find the value of a and b plzz tell me fast​

Answer 1

Correct Question:

• If 0 and 1 are the zeroes of the polynomial p(x) 2x³ - 3x² + ax + b then find the value of a and b.

Given:

• 0 and 1 are the zeroes of the polynomial 2x³ - 3x² + ax + b.

To Find:

• Value of a and b

Solution:

Let p(x) = 2x³ - 3x² + ax + b

★Case I :

0 is zero of the p(x) = 2x³ - 3x² + ax + b

Now,

→ p(0) = 2(0)³ - 3(0)² + a(0) + b

→ p(0) = 0 - 0 + 0 + b = 0

→ p(0) = b = 0 --(1)

★Case II :

1 is zero of the p(x) = 2x³ - 3x² + ax + b

Now,

→ p(1) = 2(1)³ - 3(1)² + a(1) + b

→ p(1) = 2 - 3 + a + b = 0

→ p(1) = -1 + a + 0 = 0 [From eq 1]

→ p(1) = a = 1

Hence,

• a = 1
• b = 0

Answer 2

Correct Question

• If 0 and 1 are the zeroes of the polynomial f(x) = 2x³ - 3x² + ax + b, then find the value of a and b.

⠀

Given

• Polynomial f(x) = 2x³ - 3x² + ax + b.
• Two zeroes of the polynomial are 0 and 1.

⠀

To find

• Value of a and b.

⠀

Solution

• Let us consider two cases.

⠀

$\large{\boxed{\boxed{\sf{Case\: I}}}}$

⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀When f(0) = 0

⠀

→ f(0) = 2(0)³ - 3(0)² + a(0) + b

→ f(0) = (2 × 0) - (3 × 0) + 0 + b

→ f(0) = 0 - 0 + b

→ f(0) = b

⠀

★ Putting f(0) = 0, we get

$\bf{\boxed{\longrightarrow{\green{b = 0}}}}$⠀⠀.....[1]

⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀

$\large{\boxed{\boxed{\sf{Case\: II}}}}$

⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀When f(1) = 0

⠀

→ f(1) = 2(1)³ - 3(1)² + a(1) + b

→ f(1) = (2 × 1) - (3 × 1) + a + b

→ f(1) = 2 - 3 + a + b

→ f(1) = -1 + a + b

⠀

★ Putting p(1) = 0, we get

→ -1 + a + b = 0

→ a + b = 1

⠀⠀

★ From eq[1]

→ a + 0 = 1

$\bf{\boxed{\longrightarrow{\green{a = 1}}}}$

⠀

Hence,

• Value of a = 1
• Value of b = 0

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