Ankur and Ranjan start a new business together. The amount invested by both partners together is given by the polynomial p(x) = 4x 2 + 12x + 5, which is the product of their individual shares.
i) Find the total amount invested by both, if x = 1000 .
ii) Find the value of x, if the total amount invested is equal to 0 .
Answers
Answer:
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Answer:
The correct answers are i) 40006
ii) x = -5/2 or x = -1/2
Step-by-step explanation:
Given data
⇒ Ankur and Ranjan started a business. The amount invested by both partners together is given by a polynomial p(x) = 4x²+ 12x + 5
⇒ p(x) is product of their individual shares
⇒ find factors of p(x)
⇒ p(x) = 4x² + 12x + 5
= 4x² + 2x + 10x + 5 [ 12x = 10x + 2x ]
= 2x (2x +1) + 5 (2x +1)
= (2x +5) (2x +1)
⇒ p(x) is product of (2x +5) and (2x +1)
⇒ (2x +5) and (2x +1) are the individual shares of Ankur and Ranjan
i) Find the total amount invested by both, if x = 1000
⇒ if x = 1000
⇒ the total amount invested by both = sum of individual shares
= 2x + 5 + 2x + 1 = 4x + 6
(x = 1000) ⇒ 4(1000) + 6 = 4000 + 6 = 4006
ii) Find the value of x, if the total amount invested is equal to 0
⇒ if total amount invested is equals to 0
⇒ p(x) = 0
⇒ (2x +5) (2x +1) = 0
⇒ 2x + 5 = 0 or ⇒ 2x + 1 = 0
2x = -5 2x = -1
x = -5/2 x = -1/2
⇒ x = -5/2 or x = -1/2