Question

If the alpha and beta are the zeros of the polynomial X square + 8 x + 6 find the value of Alpha minus beta

Answer 1

Answer :

    α - β = ± 2√10

Solution :

The given polynomial is

    P(x) = x² + 8x + 6

If α and β be the zeroes of P(x), by the relation between zeroes and coefficients, we get

  α + β = - 8 .....(i)

  αβ = 6 .....(ii)

Now, (α - β)²

  = (α + β)² - 4αβ

  = (- 8)² - (4 × 6)

  = 64 - 24

  = 40

⇒ (α - β)² = 40

⇒ α - β = ± √40

⇒ α - β = ± 2√10

Answer 2

alpha and beta are Zeroes of

X^2 + 8 x + 6

We know that sum of zeroes ( alpha + beta) = - ( coefficent of x)/ coefficent of x^2

So alpha + beta = - 8

We know that product of zeroes ( alpha× beta) = constant /coefficient of x^2

So alpha× beta = 6

We know that ( a- b)^2 = ( a+ b)^2 - 4ab

a- b= +-√( a+ b)^2 - 4 ab

So alpha - beta =+- √( alpha + beta)^2 - 4 × alpha × beta

= +-√( -8)^2 - 4(6)

= +-√(64 - 24)

= +-√40

= +-2√ 10

THANKS

✌✌✌✌Dr.Dhruv✌✌✌✌✌

✌✌✌✌Sr.Chairman of R.esdnick✌✌