Question

If m and n are the zeros of p(x) = x2+x+1,then find the value of 1/m+1/n*.

Answer 1

$\large\bf\underline \blue {To \: \mathscr{f}ind:-}$

• we need to find the value of 1/m + 1/n

$\huge\bf\underline \red{ \mathcal{S}olution:-}$

$\bf\underline{\purple{Given:-}}$

• m and n are Zeroes of polynomial x² + x + 1

p(x) = x² + x + 1

• a = 1
• b = 1
• c = 1

We know that,

• Sum of zeroes = -b/a

↛ m + n = -1/1

↛ m + n = -1⠀⠀.....1)

• Product of zeroes = c/a

↛ mn = 1/1

↛ mn = 1⠀⠀⠀......2)

Now,

• Value of 1/m + 1/n is :-

» 1/m + 1/n = (n + m)/mn

• From equations 1) and 2)

» 1/m + 1/n = -1/1

» 1/m + 1/n = - 1

Hence,

• » Value of 1/m + 1/n is -1

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