Question

Compute the zeroes of the polynomial 4x^2 – 4x – 8. Also, establish a relationship between the zeroes and coefficients.

Answer 1

Answer:

4x^2-4x-8=0

a=4. b=-4 c=-8

4x^2-(8-4)x-8=0

4x^2-8x+4x-8=0

4x(x-2)+4(x-2)=0

(4x+4)(x-2)=0

4x+4=0;. x-2=0

x=-1. x=2

relation between zeroes and cofficient

sum of zeroes =. -b/a

-1+2 =. -(-4)/4

1. =. 1

product of zeroes.=. c/a

-1.2 =. -8/4

-2. =. -2

Answer 2

GIVEN :–

• Quadratic polynomial is 4x² - 4x - 8 = 0

TO FIND :–

• Zero's of quadratic polynomial = ?

• Establish a relationship between the zeroes and coefficients.

SOLUTION :–

• According to the question –

$\\ \implies { \bold{ 4{x}^{2} - 4x - 8 = 0}}$

• Splitting Middle term –

$\\ \implies { \bold{ 4{x}^{2} - 8x + 4x - 8 = 0}}$

$\\ \implies { \bold{ 4x(x - 2) + 4(x - 2) = 0}}$

$\\ \implies { \bold{ (4x + 4)(x - 2) = 0}}$

$\\ \implies { \bold{ x = - 1 \: \: , \: \: 2}}$

VERIFICATION :–

$\\ \longrightarrow \: \: { \bold{ sum \: \: of \: \: roots = - \dfrac{b}{a} }}$

$\\ \implies \: \: { \bold{ 2 + ( - 1) = - (\cancel\dfrac{ - 4}{4} )}}$

$\\ \implies \: \: { \bold{ 1 = 1 \: \: \: \: \: \: \: \: \: (verified)}}$

$\\ \longrightarrow \: \: { \bold{ product \: \: of \: \: roots = \dfrac{c}{a} }}$

$\\ \implies \: \: { \bold{ 2 . ( - 1) = (\cancel\dfrac{ -8}{4} )}}$

$\\ \implies \: \: { \bold{ - 2 = - 2 \: \: \: \: \: \: \: \: \: (verified)}}$