It'o and I are the 2exces of the polynom
Hial f(x) = 2x² – 3x2 + ax + b then find the vakre
of a and b
Answers
EXPLANATION.
0 and 1 are the zeroes of the polynomial,
⇒ f(x) = 2x³ - 3x² + ax + b.
As we know that,
⇒ F(x) = 0.
Put the value of f(x) = 0 in equation, we get.
⇒ f(x) = 2x³ - 3x² + ax + b.
⇒ f(0) = 2(0)³ - 3(0)² + a(0) + b = 0.
⇒ 0 - 0 + 0 + b = 0.
⇒ b = 0.
As we know that,
⇒ F(x) = 1.
Put the value of f(x) = 1 in equation, we get.
⇒ F(x) = 2x³ - 3x² + ax + b.
⇒ 2(1)³ - 3(1)² + a(1) + b = 0.
⇒ 2 - 3 + a + b = 0.
⇒ -1 + a + b = 0.
⇒ a + b = 1.
Put the value of b = 0 in equation, we get.
⇒ a + 0 = 1.
⇒ a = 1.
Values of A = 1 & B = 0.
Answer:
- 0 and 1 are roots of polynomial
- Find the value of a and b
• According to the Question :
⇢ f(x) = 2x³ - 3x² + ax + b
⇢ f(x) = 0
- Putting the value of x = 0
⇢ f(0) = 2x³ - 3x² + ax + b = 0
⇢ 2(0)³ - 3(0)² + a(0) + b = 0
⇢ 0 - 0 + 0 + b = 0
⇢ b = 0 ⠀⠀⠀⠀— eq. ( I )
⠀⠀⠀⠀⠀───────────────
⇢ f(x) = 2x³ - 3x² + ax + b
⇢ f(x) = 0
- Putting the value of x = 1
⇢ f(1) = 2x³ - 3x² + ax + b = 0
⇢ 2(1)³ - 3(1)² + a(1) + b = 0
⇢ 2 - 3 + a + b = 0
- Putting the value of b from eq. ( I )
⇢ - 1 + a + 0 = 0
⇢ - 1 + a = 0
⇢ a = 1
∴ Values of a and b is 1 and 0 respectively.