## if alpha [tex] \alpha and \beta are the zeroes \: of \: the \: polynomial \: 2 x { + 5x + 1 \: }^{2} then \: the \: value \: of \alpha

Question

if alpha

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1 month 2021-10-28T00:11:12+00:00 2 Answers 0 views 0

1. • A quadratic polynomial 2x² + 5x + 1

For a quadratic polynomial ax² + bx + c, if the zeroes are α and β

Compare 2x² + 5x + 1 with ax² + bx + c

• a = 2
• b = 5
• c = 1

Now:-

Hence;

α + β + αβ = – 2

Explanation

Compare given equation 2x² + 5x + 1 with ax² + bx + c , we get ,

• a = 2 , b = 5 , c = 1

also given α and β are zeroes of polynomial .

Let ,

Sum of zeroes , α + β = -b/a = -(5)/2

α + β = – ⁵/₂ … (1)

Product of zeroes , αβ = c/a = (1)/(2)

αβ = ¹/₂ … (2)

Now our required ,

α + β + αβ

⇒ ( α + β ) + ( αβ )

⇒ ( – ⁵/₂ ) + ( ¹/₂ ) [ From (1) & (2) ]

⇒ ( ⁻ ⁵ ⁺ ¹/₂ )

⇒ ⁻⁴/₂

– 2