Question

verify the zeros of the polynomial g(x) = 3x²- 2 , x =2/root 3, - 2/ root 3
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Answer 1

Correct question :-

Verify the relationship between zeros and coefficients of the polynomial g(x) = 3x²- 2 where the zeros x =2/√3, - 2/√3.

Solution :-

◘ The given polynomial is :

3x² - 4

→ 3x + 0x - 4

In the given polynomial,

a = 3

b = 0

c = -4

Let the zeros of the given polynomial be x and y.

$\sf{x=\dfrac{2}{\sqrt{3}}}$

$\sf{y=\dfrac{-2}{\sqrt{3}}}$

_____________________

Sum of the zeros = -b/a

→ Sum = -(0) / 3

→ Sum = 0

_____________

$\sf{x+y=\dfrac{2}{\sqrt{3}}+ \dfrac{-2}{\sqrt{3}}}$

$\sf{x+y=\dfrac{2}{\sqrt{3}}- \dfrac{2}{\sqrt{3}}}$

$\sf{\to x+y=0}$

_____________________

Product of the zeros = c/a

→ Product = -4/3

_____________

$\sf{xy= \dfrac{2}{\sqrt{3}} \times \dfrac{-2}{\sqrt{3}}}$

$\sf{\to xy=\dfrac{-4}{3}}$

_____________________

Thus, verified.

Hope this helps ツ

Answer 2

Step-by-step explanation:

Correct question :-

Verify the relationship between zeros and coefficients of the polynomial g(x) = 3x²- 2 where the zeros x =2/√3, - 2/√3.

Solution :-

◘ The given polynomial is :

3x² - 4

→ 3x + 0x - 4

In the given polynomial,

a = 3

b = 0

c = -4

Let the zeros of the given polynomial be x and y.

\sf{x=\dfrac{2}{\sqrt{3}}}x=

3

2

\sf{y=\dfrac{-2}{\sqrt{3}}}y=

3

−2

_____________________

Sum of the zeros = -b/a

→ Sum = -(0) / 3

→ Sum = 0

_____________

\sf{x+y=\dfrac{2}{\sqrt{3}}+ \dfrac{-2}{\sqrt{3}}}x+y=

3

2

+

3

−2

\sf{x+y=\dfrac{2}{\sqrt{3}}- \dfrac{2}{\sqrt{3}}}x+y=

3

2

−

3

2

\sf{\to x+y=0}→x+y=0

_____________________

Product of the zeros = c/a

→ Product = -4/3

_____________

\sf{xy= \dfrac{2}{\sqrt{3}} \times \dfrac{-2}{\sqrt{3}}}xy=

3

2

×

3

−2

\sf{\to xy=\dfrac{-4}{3}}→xy=

3

−4

_____________________

Thus, verified.