Question

find the zeros of each of the following quadratic polynomials and verify the relationship between the zeros and their coefficients f (x)=x^2-2x-8

Answer 1

You can refer to the picture for the answer

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

f(x) = x² - 2x - 8

= x² - 4x + 2x - 8

= x(x - 4) + 2(x - 4)

= (x + 2)(x - 4)

(x + 2) = 0

x = -2

(x - 4) = 0

x = 4

${\boxed{\sf\:{Zeroes\;are\;-2\;and\;4}}}$

★Verification :-

α = -2

β = 4

α + β = -2 + 4 = 2

α × β = (-2) × (4) = -8

As per question a = 1, b = -2 and c = -8

★Hence,

$\tt{\rightarrow\dfrac{-b}{a}=\dfrac{-(-2)}{1}=2}$

${\rightarrow\dfrac{c}{a}=\dfrac{-8}{1} =-8}$

$\boxed{\begin{minipage}{11 cm} Therefore, \\ \\ \ Sum\;of\;zeroes\;of\; polynomial\;is\;2 \\ \\ Product\;of\;zeroes\;of\; polynomial\;is\; -8 \\ \\ \bold{Hence\;Verified} \end{minipage}}$