Question

Find the zeros of the quadratic polynomial x^2-6 and verify the relationship between the zeros and the coefficients

Answer 1

Answer:

Step-by-step explanation:

Hi there !!

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]

Hope this helps you !