Question

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

Answer 1

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.

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

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

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

Answer 2

Correction:

If @ and ß are the zeros of the polynomials 2x²-4x+5,then find the value of (@+ß)².

Answer:

Let f(x) be the given Quadratic Polynomial

f(x)=2x²-4x+5

Here,

On comparing with ax²+bx+c,we get:

a=2,b= -4 and c=5

Now,

Sum of zeros:

@+ß= -b/a= -(-4)/2=2

Product of zeros:

@ß=c/a=5/2

Also now,

(@+ß)²

=(2)²

=4

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