Question

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$\bold{\huge{Question:-}}}$Divide :- 5x(x^2 - x + 1) - (9 + 4x^2) by 4x - 1. Hence write the degree of the Quotient and the remainder. (Polynomial)

$\bold{\huge{Question:-}}}$ Find x if 2^(2x+2) = 4^(2x-1)

Answer 1

Step-by-step explanation:

(1)

Given, f(x) = 5x(x² - x + 1) - (9 + 4x²)

                = 5x³ - 5x² + 5x - 9 - 4x²

                = 5x³ - 9x² + 5x - 9.

Given, g(x) = 4x - 1.

Long Division Method:

4x - 1) 5x³ - 9x² + 5x - 9 (5x²/4 - 31x/16 + 49/64

         5x³ - 31x²/4

         --------------------------

                -31x²/4 + 5x - 9

              -31x²/4 + 31x/16

         -----------------------------

                             49x/16 - 9

                             49x/16 - 49/64

         --------------------------------------

                                            -527/64

         

∴ Quotient = (5x²/4)  - (31x/16) + (49/64, Remainder = -527/64.

Therefore:

Highest Degree of Quotient = 2.

Degree of Remainder = 0.

(2)

Given: 2^(2x + 2) = 4^(2x - 1)

⇒ 2^(2x + 2) = [2^2)^(2x - 1)

⇒ 2^(2x + 2) = 2^(4x - 2)

⇒ 2x = 4x - 4

⇒ -2x = -4

⇒ x = 2.

Therefore, the value of x = 2.

Hope it helps!

Answer 2

Answer:

x=2

Step-by-step explanation:

I hope it's help you