13. Ankur and Ranjan start a new business together. The amount invested by both partners together is given by the polynomial p(x) = 4x² + 12x + 5, which is the product of their individual shares.
1) Find the total amount invested by both, ifx = 1000
2) Find the value of x, if the total amount invested is equal to 0.
Answers
Answer:
Product of their individual sale =(2x+5)+(2x+1)
1) 4012005
2) value of x is -5/2 or -1/2
Step-by-step explanation:
p(x) = 4x^2+12x+5 = 4x^2+10x+2x+5 = 2x (2x+5)+(2x+5)
=(2x+5)+(2x+1)
1) p(1000)= 4×1000^2+12×1000+5= 4000000+12000+5=4012005
2) (2x+5) (2x+1)=0
if product of two number is zero then they are individually zero
2x+5=0
x=-5/2
and 2x+1 =0
x=-1/2
Answer:
1) 4012005
2) -5/2 or -1/2
Step-by-step explanation:
The amount invested by both partners together is given by the polynomial,
p(x)=4x^2+12x+5
It can be written as the product of their individual shares. So,
p(x)= (2x+5)(2x+1). ( By splitting the middle term method)
1. If x=1000, total amount invested by both is given by,
p(1000)= (2*1000+5)(2*1000+1)
p(1000)= (2*1000+5)(2*1000+1) = (2000+5)(2000+1)
p(1000)= (2*1000+5)(2*1000+1) = (2000+5)(2000+1) =2005*2001
p(1000)= (2*1000+5)(2*1000+1) = (2000+5)(2000+1) =2005*2001 =4012005
2. If the total amount invested is equal to 0 then the value of x is given by
p(x)=0
p(x)=0(2x+5)(2x+1)=0
p(x)=0(2x+5)(2x+1)=02x+5=0 or 2x+1=0
p(x)=0(2x+5)(2x+1)=02x+5=0 or 2x+1=02x= -5. or 2x= -1
p(x)=0(2x+5)(2x+1)=02x+5=0 or 2x+1=02x= -5. or 2x= -1x=-5/2. or x=-1/2
x= -5/2 or -1/2