Sorry I made a typo. Here’s the question.
According to the quadratic discriminant, the product and sum of two numbers, which is k, cannot equal in [tex]0\ \textless \ k\ \textless \ 4[/tex]. Explain the reason.
The product of two numbers can only be 0 if either the multiplicand or the multiplier itself will be 0 . So , our sum as well as one of our terms of addition is 0 . 0 is the additive identity of all types of numbers . So , a number that is added to 0 to give 0 cannot be other than 0 .
In this case ,
k + k = k × k
⟹ 2k = k²
By replacing k by 0 , we get :—
0 + 0 = 0 × 0
⟹ 2(0) = 0²
⟹ 0 = 0
The other possible answer is 2 . Ramanujan stated that 2 is a unique and the only known number whose product with itself is equal to its sum with itself i.e.
2 + 2 = 2 × 2
⟹ 2(2) = 2²
⟹ 4 = 4
This satisfies the above equation where only the result is k i.e.
[tex]\large{ \underline{ \underline{ \sf{ \color{cyan}{}{REQUIRED \: ANSWER:-} }{} }{} }{} }{}[/tex]
The Product Of 2 numbers can only be 0 if either the multiplication itself be 0
A number added or Multiplied gives other than 0
Consider the Example :-
[tex] \rightarrow{k + k = k \times k}{} \\ \\ \rightarrow{2k = {k}^{2} }{} \\ \\ \rightarrow{giving \: k = 0}{} \\ \\ \sf{ \rightarrow{0 = 0 \times 0 = 0}{} }{}[/tex]
The product of two numbers can only be 0 if either the multiplicand or the multiplier itself will be 0 . So , our sum as well as one of our terms of addition is 0 . 0 is the additive identity of all types of numbers . So , a number that is added to 0 to give 0 cannot be other than 0 .
In this case ,
k + k = k × k
⟹ 2k = k²
By replacing k by 0 , we get :—
0 + 0 = 0 × 0
⟹ 2(0) = 0²
⟹ 0 = 0
The other possible answer is 2 . Ramanujan stated that 2 is a unique and the only known number whose product with itself is equal to its sum with itself i.e.
2 + 2 = 2 × 2
⟹ 2(2) = 2²
⟹ 4 = 4
This satisfies the above equation where only the result is k i.e.
a + b = ab , where a = b
or
a + a = a × a
⟹ 2a = a²