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If alpha and beta are the zeroes of the polynomial 2x²-4x+5,then find the value of alphaand beta whole square

Answer»

Correct question: If α and β are the zeroes of the polynomial 2x² - 4x + 5, then FIND the value of (α + β)².

Answer:

(α + β)² = 4

Step-by-step EXPLANATION:

Given polynomial ;

2x² - 4x + 5, on comparing the given equation with ax² + bx + c,

  • a = 2
  • b = (-4)
  • c = 5

We know that ;

SUM of zeroes =\bf - \dfrac{b}{a}

⇒ α + β = -(-4)/2

⇒ α + β = 4/2

⇒ α + β = 2

Product of zeroes = \bf \dfrac{c}{a}

⇒ αβ = 5/2

Now,

( \alpha + \beta ) {}^{2} \\ \\ \implies (2) {}^{2} \\ \\\implies 4

HENCE, the answer is 4.

_______________________

\large{\underline{\underline{\mathfrak{\heartsuit \: Extra \: Information: \: \heartsuit}}}}

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

  • α + β = \sf - \dfrac{b}{a}
  • αβ = \sf \dfrac{c}{a}


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