Dheeraj sais"The zeros of the polynomial x2-1 are -1 and 1. Is he correct? justify your answer?
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Let
![\alpha = - 1 \: and \: \beta = 1 \alpha = - 1 \: and \: \beta = 1](https://tex.z-dn.net/?f=+%5Calpha++%3D++-+1+%5C%3A+and+%5C%3A++%5Cbeta++%3D+1)
be the zeros of the polynomial
![{x}^{2} - 1 {x}^{2} - 1](https://tex.z-dn.net/?f=+%7Bx%7D%5E%7B2%7D++-+1)
a = 1, b = 0, c = -1
Then,
![\alpha + \beta = \frac{ - b}{a} \\ = > - 1 + 1 = \frac{0}{1} \\ = > 0 = 0 \\ = > l.h.s = r.h.s \\ and \\ \: \alpha \beta = \frac{c}{a} \\ = > - 1 \times 1 = \frac{ - 1}{1} \\ = > - 1 = - 1 \\ = > l.h.s \: = \: r.h.s \alpha + \beta = \frac{ - b}{a} \\ = > - 1 + 1 = \frac{0}{1} \\ = > 0 = 0 \\ = > l.h.s = r.h.s \\ and \\ \: \alpha \beta = \frac{c}{a} \\ = > - 1 \times 1 = \frac{ - 1}{1} \\ = > - 1 = - 1 \\ = > l.h.s \: = \: r.h.s](https://tex.z-dn.net/?f=+%5Calpha++%2B++%5Cbeta++%3D++%5Cfrac%7B+-+b%7D%7Ba%7D++%5C%5C++%3D++%26gt%3B++-+1+%2B+1+%3D++%5Cfrac%7B0%7D%7B1%7D++%5C%5C++%3D++%26gt%3B+0+%3D+0+%5C%5C+%3D++%26gt%3B++l.h.s+%3D+r.h.s+%5C%5C+++and+%5C%5C++%5C%3A++%5Calpha++%5Cbeta++%3D++%5Cfrac%7Bc%7D%7Ba%7D++%5C%5C++%3D++%26gt%3B++-+1+%5Ctimes+1+%3D++%5Cfrac%7B+-+1%7D%7B1%7D++%5C%5C++%3D++%26gt%3B++-+1+%3D++-+1+%5C%5C++%3D++%26gt%3B+l.h.s+%5C%3A++%3D++%5C%3A+r.h.s)
Therefore, the statement is correct.
be the zeros of the polynomial
a = 1, b = 0, c = -1
Then,
Therefore, the statement is correct.
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