If alpha and beta are zeros of the polynomial 3x²+5x+2, find the value of 1/alpha + 1/beta and alpha² + beta²
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Answer:
24 is the answer
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★ Answer
- α and β are Zeroes of Polynomial 3x²+5x+2
As We know the different relations b/w zeroes of the polynomial using α+β = -b/a and αβ = c/a as:
→ α + β = -b/a
→ α + β = -5/3 [1]
→ αβ = c/a
→ αβ = 2/3 [2]
As We got the different relations between zeroes as well. Now We can find values,
→ 1/α + 1/β
→ α + β/αβ
→ (-5/3) / (2/3)
→ -5×3/2×3
→ -5/2
Finally, we're going to find the value of alpha² + beta² as:
→ α² + β² = (α+β)²-2αβ
→ (-5/3)² - 2 × 2/3
→ 25/9 - 4/3
→ 25-12/9
→ 13/9
Hence,
Above we have got all required values.