Question

Find the zeroes of the polynomial x2 + x - 6 and verify the relationship
between the zeroes and its coefficients.​

Answer 1

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$x^2+x-6$

$x^2-2x+3x-6$

$(x^2-2x)+(3x-6)$

$x(x-2)3(x-2)$

(x-2)(x+3) are the zeros

x -2=0                        x+3=0

x = 2                           x= -3

let α be 2 and β be -3

here

a = 1 , b = 1 ,c = -6

$\alpha+\beta$= $\frac{-b}{a}$

2  + -3 =  $\frac{-1}{1}$

$\boxed{-1\:=\:-1}$  

$\alpha\beta$= $\frac{c}{a}$

2*-3 =  $\frac{-6}{1}$

$\boxed{-6\:=\:-6}$  

hece we founded the two zeros and verified with zeroes and its coefficients.​