Question

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

Answer 1

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