Given: n2 + 4n = 0 and n = 0, ndash;2, ndash;4 On substituting n = 0 in L.H.S. of the given equation, we get: nbsp;(0)2 + 4(0) = 0 #8658; #160;L. ...

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Formation of a Quadratic Equation From It's Roots

n2+4 n=0, n=...

Question

n² + 4n = 0, n = 0, –2, –4

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Solution

Given: n² + 4n = 0 and n = 0, –2, –4

On substituting n = 0 in L.H.S. of the given equation, we get:
(0)² + 4(0)
= 0
$\Rightarrow$ L.H.S. = R.H.S.
Thus, n = 0 satisfies the given equation.
Therefore, n = 0 is a root of the given quadratic equation.

On substituting n = –2 in L.H.S. of the given equation, we get:
(–2)² + 4(–2)
= 4 – 8
= – 4
$\Rightarrow$ L.H.S. $\neq$ R.H.S.
Thus, n = –2 does not satisfy the given equation.
Therefore, n = –2 is not a root of the given quadratic equation.

On substituting n = – 4 in L.H.S. of the given equation, we get:
(–4)² + 4(–4)
= 16 – 16
$\Rightarrow$ L.H.S. = R.H.S.
Thus, n = – 4 satisfies the given equation.
Therefore, n = – 4 is a root of the given quadratic equation.

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