Question

Find the zeros of the quadratic polynomial x square - 2 x minus 8 and verify the relationship between the zeros and its coefficients

Answer 1

relationship between zeroes and coefficients are verified

Answer 2

Answer:

$\green { -2 \: and \: 4 \: are \: zeroes \: of \: polynomial }$

Step-by-step explanation:

$Given \: quadratic \: polynomial \:x^{2}-2x-8$

/* Splitting the middle term,we get

$= x^{2} - 4x + 2x - 8 \\= x(x-4) + 2(x-4)\\=(x-4)(x+2)$

p(x) = x² - 2x - 8 is zero when x - 4 = 0 Or x +2 = 0

i.e ., when x = 4 Or x = -2 .

$\green { the \: zeroes \:of \: x^{2}-2x-8 \:are \: 4 \:and \: -2}$

Relationship between Zeroes and Coefficients:

Compare x² - 2x - 8 with ax² + bx + c ,we get

$a = 1 ,\: b = -2 , \: c = -8$

$\pink { The\:sum \: of \: the \: zeroes = 4 + (-2)}$

$\pink {= \frac{-(-2)}{1} }=\pink { \frac{-(coefficient \:of\:x)}{coefficient \: of \:x^{2}} }$

$\orange { Product \: of \: the \: zeroes = 4\times (-2) }$

$\orange { = -8 = \frac{-8}{1} }= \orange {\frac{constant}{coefficient \:of \: x^{2}}}$

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