Question

Find zeros of the quadratic polynomial & verify the realation between the zeroes & the coefficient of x2-2x-8

Answer 1

Answer:

$\boxed{\red{\sf Zeroes = 4 ,(-2) }}$

Step-by-step explanation:

We need to find out the zeroes of the quadratic polynomial and to verify the realtionship between the zeroes and coefficients. The given quadratic equation is ,

$\sf\red{\dashrightarrow } x^2-2x -8 = 0$

• 》For finding the zeroes of the quadratic equation, we can factorise it , and then equate with 0 , to find the roots .

$\sf\dashrightarrow x^2-2x -8 = 0 \\\\\sf\dashrightarrow x^2 -4x +2x -8 = 0 \\\\\sf\dashrightarrow x ( x -4)+2(x-4)=0 \\\\ \sf\dashrightarrow ( x -4)(x+2) = 0 \\\\\sf\dashrightarrow \boxed{\pink{\sf x = 4 , -2 }}$

• 》Now we know that the Standard form of a quadratic equation is qx² + px + c = 0. And wrt Standard form ,the sum of zeroes is -b/a and the product of zeroes is c/a .

$\sf\dashrightarrow Sum_{Zeroes}=\dfrac{-b}{a} \\\\\sf\dashrightarrow 4-2 =\dfrac{ -(-2)}{1} \\\\\sf\dashrightarrow\boxed{\red{\sf 2 = 2 }}$

$\rule{200}2$

$\sf\dashrightarrow Product_{Zeroes}=\dfrac{c}{a} \\\\\sf\dashrightarrow 4\times (-2) =\dfrac{ -(8)}{1} \\\\\sf\dashrightarrow\boxed{\red{\sf -8 = -8 }}$

■ Hence verified the realtionship between the zeroes and coefficients .

$\rule{200}2$