Question

2x4 - 7x3 – 13x2 +63x – 45​

Answer 1

Answer:

2x4 - 7x3 – 13x2 +63x – 45​

Step-by-step explanation:

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Answer 2

Appropriate Question:

• 2x⁴- 7x³- 13x² + 63x- 45

Required Solution:

• Let f(x) = 2x⁴- 7x³ -13x² + 63x- 45

Constant term = -45

• Factors of -45 are ±1, ±3, ±5, ±9, ±15, ±45

Here coefficient of x^4 is 2. So possible rational roots of f(x) are

±1, ±3, ±5, ±9, ±15, ±45, ±1/2,±3/2,±5/2,±9/2,±15/2,±45/2

Let x - 1 = 0 or x = 1

f(1) = 2(1)⁴- 7(1)³- 13(1)2 + 63(1) -45

f(1) = 2- 7-13 + 63-45

f(1) = 0

f(x) can be written as,

f(x) = (x-1) (2x3 – 5x2-18x +45)

or f(x) =(x-1)g(x) …(1)

Let x - 3 = 0 or x = 3

f(3) = 2(3)⁴- 7(3)³- 13(3)² + 63(3) – 45

f(3) = 162 – 189 – 117 + 189 – 45= 0

f(3) = 0

Now, we are available with 2 factors of f(x), (x- 1) and (x – 3)

Here g(x) = 2x²

(x-3) + x(x-3) -15(x-3)

Taking (x-3) as common

= (x-3)(2x2+ x- 15)

=(x-3)(2x2+6x-5x -15)

= (x-3)(2x-5)(x+3)

= (x-3)(x+3)(2x-5) ….(2)

From (1) and (2)

f(x) =(x-1) (x-3)(x+3)(2x-5)

• Hence, the required answer is f(x) =(x-1) (x-3)(x+3)(2x-5)