Question

If alpha and beta be the zeros of X^2-2x-8,then find the value of alpha square +beta square

Answer 1

Answer:

20

Step-by-step explanation:

We know,

     quadratic polynomials / equations represent sum and product of their roots as S and P in the equation in form of x^2 - Sx + P = 0.

Therefore, here, in polynomial x^2 - 2x - 8

   Sum of roots = 2

  Product of roots = - 8

Here,

⇒ α^2 + β^2

⇒ α^2 + β^2 + 2αβ - 2αβ

⇒ ( α + β )^2 - 2αβ            { using a^2 + b^2 + 2ab = ( a + b )^2}

⇒ ( sum of roots )^2 - 2( product of roots )

⇒ ( 2 )^2 - 2( - 8 )

⇒ 4 - 2( - 8 )

⇒ 4 + 16

⇒ 20

Answer 2

Answer:

20

Step-by-step explanation:

Given that -

• α and β are the zeroes of the quadratic polynomial x²- 2x - 8.

We know that,

Quadratic polynomial are represented in the form of ax² + bx + c. Here,

• a = 1
• b = - 2
• c = - 8

Sum of zeroes = $\sf \dfrac{-(coefficient \: of \: x)}{coefficient \: of \: x^2}$

⇒ α + β = $\dfrac{-(-2)}{1}$

⇒ α + β = 2

Product of zeroes = $\sf \dfrac{constant \: term}{coefficient \: of \: x^2}$

⇒ α β = $\dfrac{-8}{1}$

⇒ α β = - 8

We need to find : α² + β²

⇒ α² + β²

⇒ α² + β² + 2αβ - 2αβ

[ Identity used : x² + y² + 2xy = (x + y)².]

⇒ (α + β)² - 2αβ

⇒ (2)² - 2 (-8)

⇒ 4 + 16

⇒ 20

Hence, the answer is 20.