Answer :
The Quadratic equation f(n) = n2 - 2n, the value of n is correct in option A & E.
According to the question, given that
f(n) = n2 - 2n
when,
(A) n = 2
f(n) = n2 - 2n
f(2) = 2^2 - 2*2
= 4 - 4
= 0
Hence, f(2) = 0 proved
(B) n = -2
f(n) = n2 - 2n
f(-2) = (-2)^2 - 2(-2)
= 4 + 4
= 8
f(- 2) = 0 not proved
(C) n = 1
f(n) = n2 - 2n
f(1) = 1^2 - 2*1
= 1 - 2
= -1
f(1) = 3 not proved
(D) n= 5
f(n) = n2 - 2n
f(5) = 5^2 - 2*5
= 25 - 10
= 15
f(5) = 35 not proved
(E) n = - 4
f(n) = n2 - 2n
f(- 4) = (-4)^2 - 2*(- 4)
= 16 + 8
= 24
Hence, f(- 4) = 24 proved
Therefore, the given quadratic equation f(n) = n2 - 2n, the value of n is correct in A and E option.
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x2 (a 0) for an equation to be a quadratic equation. The x2 term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term. The numerical values of a, b, and c are typically expressed as integral values rather than fractions or decimals.
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