Question

Xsquare - 3
Find the zeroes of the polynomial and find sum and product
Step by step please​

Answer 1

Step-by-step explanation:

x^2 - 2x - x + 2

x(x - 2) - 1(x-2) = 0

(x-1)(x-2) = 0

x= 1 , 2

sum of zeroes = a +b = -b/a

= 1 + 2 = 3 = -(-3/1) = 3

product of zeroes = ab = c/a

= 1 x 2 = 2 = 2/1 = 2

Answer 2

Solution :

We have p(x) = x² - 3

Zero of the polynomial p(x) = 0

So;

$\longrightarrow\tt{x^{2} -3=0}\\\\\longrightarrow\tt{x^{2} =3}\\\\\longrightarrow\tt{x=\pm\sqrt{3}$

∴ The α = √3 and β = -√3 are the zeroes of the polynomial.  

Now;

$\underline{\boldsymbol{Sum\:of\:the\:zeroes\::}}}$

$\mapsto\tt{\alpha +\beta }\\\\\\\mapsto\tt{\sqrt{3} +(-\sqrt{3} )}\\\\\\\mapsto\tt{\sqrt{3} -\sqrt{3} }\\\\\\\mapsto\bf{0}$

$\underline{\boldsymbol{Product\:of\:the\:zeroes\::}}}$

$\mapsto\tt{\alpha \beta }\\\\\\\mapsto\tt{\sqrt{3} \times (-\sqrt{3})}\\ \\\\\mapsto\tt{\sqrt{3\times -3} }\\\\\\\mapsto\tt{-\sqrt{9} }\\\\\\\mapsto\bf{-3}$