Question

The product of four consecutive natural numbers is 840. Find the numbers
( Quadratic equation with one variable )

Answer 1

Answer:

4 numbers are 4 , 5 , 6 and 7 .

Step-by-step explanation:

Let four consecutive natural numbers are( x -2 ) , (x-1) , x and (x+1). Acordingly:-

(x-2)×(x-1) × x(x+1) = 840

(x²–2x)×(x²–1)= 840

x⁴–2x³-x²+2x-840 = 0

On putting x=6

R=1296–432–36+12–840

=1308–1308=0

(x-6)is a factor

x⁴–2x³-x²+2x-840=0

x³(x-6)+4x²(x-6)+23x(x-6)+140(x-6)=0

(x-6)(x³+4x²+23x+140) =0

⇒ x-6=0 => x =6

=1st number =x-2 = 6–2 = 4

2nd number =x-1 = 6–1 = 5

3rd number =x = 6

4th number= x+1 =6+1 = 7

Final Ans:

4 numbers are 4 , 5 , 6 and 7 .

Answer 2

this is your answer mate.