Question

find zeros of polynomial 5x2 -
6√2x + 2 verify the relationship between zeros and coefficient​

Answer 1

Answer:

The relationship between zeros and coefficients of given polynomial is verified.

Step-by-step explanation:

Polynomial = 5x² – 6√2x + 2

Find zeros of the given polynomial by factorizing the polynomial.

$\longrightarrow$ 5x² – 6√2x + 2

$\longrightarrow$ 5x² – 5√2x – √2x + 2

$\longrightarrow$ 5x(x – √2) – √2(x – √2)

$\longrightarrow$ (5x – √2)(x – √2)

Zeros will be =

$\longrightarrow$ 5x – √2 = 0

$\longrightarrow$ 5x = √2

$\longrightarrow$ x = √2/5

$\longrightarrow$ x – √2 = 0

$\longrightarrow$ x = √2

The zeros are √2/5 and √2.

______________________

Verifying the relationship of zeros and coefficients :

Let the α and β be zeros.

In the polynomial,

• a = 5
• b = -6√2
• c = 2

Sum of zeros :

$\longrightarrow$ √2/5 + √2

$\longrightarrow$ √2/5 + 5√2/5

$\longrightarrow$ 6√2/5 ---- (I)

$\longrightarrow$ α + β = -b/a

$\longrightarrow$ α + β = -(-6√2)/5

$\longrightarrow$ α + β = 6√2/5 ---- (II)

Product of zeros :

$\longrightarrow$ √2/5 × √2

$\longrightarrow$ 2/5 ---- (III)

$\longrightarrow$ α β = c/a

$\longrightarrow$ α β = 2/5 ---- (IV)

I and II are equal

III and IV are equal

Hence, the relationship between zeros and coefficients of given polynomial is verified.

Answer 2

Given :-

5x² - 6√2x + 2

To Find :-

Zeroes

Solution :-

5x² - 6√2x + 2

5x² - (5√2x + √2x) + 2

5x² - 5√2x - √2x + 2

5x(x - √2) - √2(x - √2)

(5x - √2)(x - √2)

Either

5x - √2 = 0

5x = √2

x = √2/5

Or

x - √2 = 0

x = √2

So,

α = √2/5

β = √2

α + β = -b/a

√2/5 + √2 = -(-6√2)/5

√2 + 5√2/5 = 6√2/5

6√2/5 = 6√2/5

αβ = c/a

√2/5 × √2 = 2/5

√2 × √2/5 = 2/5

(√2)²/5 = 2/5

2/5 = 2/5

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