Question

find the zeroes of the polynomial mx(x-m-1)+m^2 and verify the relation b/w zeroes and coefficients

Answer 1

Answer:

Finding Zeroes

$mx(x-m-1)+m^2\\mx^{2} - m^{2}x - mx + m^{2} \\mx(x - m) - m(x - m)\\(mx - m)(x - m)\\\\mx - m = 0\\x = m/m\\x = 1\\\\x - m = 0\\x = m$

Verification

$\alpha + \beta = m + 1\\\alpha \beta = m\\\\Also,\\\\\alpha + \beta \\= \frac{-b}{a} \\= \frac{-(-m^{2} - m)}{m} \\=\frac{m(m+1)}{m}\\= \frac{m+1}{1} \\= m+1\\\\\alpha\beta = \frac{c}{a} \\= \frac{m^{2} }{m} \\= mHence verified.$

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