Question

x square +2root2x+6 verify the relationship between the zeroes and the CO efficient s

Answer 1

Hey Mate ✌

Here's your answer friend,

==> x² + 2√2x + 6 = 0 it is a wrong question friend,


==> x² + 2√2x - 6 = 0 is the correct question.

==> x² + 3√2x - √2x - 6 = 0

==> x ( x + 3√2) -√2 (x + 3√2) = 0

==> (x - √2)(x + 3√2) = 0

==> x = √2 and x = -3√2

Now Verification ==============>

On comparing above equation, we get

a = 1, b = 2√2, c = -6

Let α = √2 and β = -3√2

==> Sum of the zeroes : α + β = -b/a

==> √2 -3√2 = -2√2/1

==> -2√2 = -2√2

==> LHS = RHS

and

Now,

Product of zeroes : αβ = c/a

==> √2 x (-3√2) = -6/1

==> -6 = -6

==> LHS = RHS

Hence, Verified ✌

⭐ Hope it helps you : ) ⭐

Answer 2

Hiii friend,

IT SEEMS YOUR QUESTION IS WRONG.

IT SHOULD BE X²+2✓2X-6

P(X) = 0

X²+2✓2X -6

=> X²+3✓2X-✓2X-6

=> X(X+3✓2) -✓2(X+3✓2)

=> (X+3✓2)(X-✓2)

=> (X+3✓2) = 0 OR (X-✓2) = 0

=> X = -3✓2 OR X = ✓2

-3✓2 and ✓2 are the two zeros of the polynomial X²+2✓2-6.

Alpha = -3✓2 and beta = ✓2


Relationship between the zeros and Coefficient.

Sum of zeros = (Alpha + Beta) = (-3✓2+✓2) = -2✓2 = -(Coefficient of X)/(Coefficient of X²).

Product of zeros = (Alpha × Beta) = (-3✓2 × ✓2) = -6✓2 = Constant term/Coefficient of X².

HOPE IT WILL HELP YOU....... :-)