Question

if alpha beta are the zeros of 3 x square - 5 x minus 2 then evaluate Alpha square plus beta square

Answer 1

Step-by-step explanation:

Given :

α and β are the zeroes of the polynomial 3x² - 5x - 2.

To find :

α² + β² ?

Solution :

We have p(x) = 3x² - 5x - 2

Sum of zeroes :

⇒ α + β = -b/a

• -(-5/3)
• 5/3

Product of zeroes :

⇒ α × β = c/a

• -2/3

Using the formula,

⇒ α² + β² = (α + β)² - 2αβ

Substituting the values we get,

⇒ α² + β² = (α + β)² - 2αβ

⇒ α² + β² = (5/3)² - 2(-2/3)

⇒ α² + β² = (25/9) + (4/3)

⇒ α² + β² = [25 × 1 + 4 × 3]/9

⇒ α² + β² = [25 + 12]/9

⇒ α² + β² = 37/9

∴ α² + β² = 37/9.

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