Question

x^2 + 2√2- 6 find the zeros of quadratic polynomial and verify the relation between the zeros​

Answer 1

Step-by-step explanation:

For zeros ,

x^2 +2√2x -6=0

→x^2 + 3√2x -√2x -6 =0

→x(x+3√2)-√2(x+3√2)=0

→(x-√2)(x+3√2)=0

→x=√2 or , -3√2

Hence , zeros of given polynomial are √2 and -3√2

Verification

1) Sum of zeros = √2-3√2= -2√2 =-(coefficient of x)/coefficient of x^2

2)Product of zeros =(-3√2)√2= -6=(constant term )/(coefficient of x^2)

Hence , verified

I hope it helped u mate ........

All the best for boards

Answer 2

Step-by-step explanation:

p(x) = x² + 2√2x - 6

We can find the zeros by factorization [ by splitting the middle terms ]

x² + 2√2x - 6

x² + 3√2x - √2x - 6

x [ x + 3√2 ] - √2 [ x+ 3√2]

[ x - √2 ] [ x+ 3√2]

the zeros are = √2 and -3√2

α = √2

β = -3√2

a = 1

b = 2√2

c = -6

Sum of zeros = √2 + -3√2 = -2√2 = -b/a [ -b/a = -2√2 ]

Product of zeros = √2 × -3√2 = - 6 = c/a [c/a = -6/1 = -6]