Question

if alpha and beta are the zeros of the polynomial f (x)= x square + x – 2 find the value of 1 by Alpha - 1 by beta

Answer 1

p(x) = x² + x - 2
Instead of alpha and beta, I'll write a and b
So, p(x) = x² + x - 2
= x² + 2x - x - 2
= x(x + 2) -1(x +2)
= (x - 1)(x +2)
x = 1 ; x = (-2)

Therefore, a = 1, b = (-2)
1/a + 1/b = 1/1 + 1/2 = 3/2

OR, if a = -2 and b = 1
1/a + 1/b = -2 +1/2 = -3/2

Answer 2

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$\mathfrak{Answer\:is}$

$p(x) = x^{2} + x - 2$

$Instead \:of \:alpha \:and \:beta, \:I'll \:write \:a \:and \:b.$

$So, p(x) = x^{2} + x - 2$

$= x^{2} + 2x - x - 2$

$= x (x + 2) - 1 (x + 2)$

$= (x - 1) (x + 2)$

$x = 1 ; x = (-2)$

$Therefore, a = 1, b = (-2)$

$\frac{1}{a} + \frac{1}{b} = \frac{1}{1} + \frac{1}{2} = \frac{3}{2}$

$Or$

$If a = (-2) and \:b = 1$

$\frac{1}{a} + \frac{1}{b} = -2 + \frac{1}{2} = \frac{-3}{2}$

$\boxed{\boxed{Hope\:This\:Helps}}$