Question

If α & β are the zeroes of the quadratic polynomial f(x) =x² -3x-2, then what is α + β equal to?

Answer 1

Answer:

x^2-3x+2 (by middle term splitting)

x^2-x-2x+2

x(x-1)-2(x-1)

(x-2)(x-1)

x-2=0, x=2

x-1=0,x=1

therefore 1,2 are roots of the equation.

sum is equal to 1+2= 3.

therefore alpha+beta= 3.

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Answer 2

$Compare \: f(x) = x^{2} - 3x - 2 \:with \\ax^{2} + bx + c , we \:get$

$a = 1 , b = -3 \:and \:c = -2$

$Given \: \alpha \: and \: \beta \: are \: two \\zeroes \: of \: f(x)$

$Sum \:of \:the \: zeroes = \frac{-b}{a}$

$\implies \alpha + \beta = \frac{-(-3)}{1} \\=3$

Therefore.,

$\red { \alpha + \beta }\green {= 3 }$

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