Question

Q) If α and ß are the zeroes of the polynomial 2x²+5x+1, then the value of α+ß+αß is :
a) -2
b) -1
c) 1
d) 3

*(please give the full explanation)*​

Answer 1

Answer

• The value of α + β + αβ = -2. ( option a )

Given

• α and β are the zeros of the quadratic polynomial 2x² + 5x + 1.

To Do

• To find the value of α + β + αβ

Step By Step Explanation

We know that α and β are the zeros of the quadratic polynomial 2x² + 5x + 1. We need to find the value of α + β + αβ. So let's do it !!

Formula Used :

• $\bigstar \underline{\boxed{ \pink{ \mathfrak{\alpha + \beta = \cfrac{ - b}{a}}}}} \\ \\ \bigstar \underline {\boxed{ \purple{ \mathfrak{\alpha \beta = \cfrac{c}{a}}}}}$

Here, 2 = a, 5 = b and 1 = c.

Substituting :

Let's substitute the formula to find the value of α + β + αβ.

$\longmapsto \sf \alpha + \beta + \alpha \beta \\ \\\longmapsto \sf ( \alpha + \beta ) + \alpha \beta \\ \\ \longmapsto \sf \bigg( \cfrac{ - 5}{2} \bigg)+ \cfrac{1}{2} \\ \\ \longmapsto \sf \cfrac{ - 5 + 1}{2} \\ \\\longmapsto \sf \cancel\cfrac{ -4}{2}\\ \\ \longmapsto\bf{ \green{- 2 }}$

Therefore, the value of α + β + αβ = -2. (option a)

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Answer 2

Step-by-step explanation:

$\large \bold \red{Question →}$

★ If α and ß are the zeroes of the polynomial 2x² + 5x + 1 , then the value of α + ß + αß is :-

• A] -2
• B] -1
• C] 1
• D] 3

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$\large \bold \red{Answer →}$

Given Polynomial :-

• 2x² + 5x + 1

To Find :-

• α + ß + αß

$\large \bold \pink{Solution →}$

Here,

• a = 2
• b = 5
• c = 1

Where,

• α and ß are zeros.

Then,

• α + ß = -5/2
• αß = 1/2

Now,

• Finding :- α + ß + αß

➡ -5/2 + 1/2

➡ ( -5+1 ) / 2

➡ -4 / 2

➡ -2

Hence,

• Option 1, [ -2 ] is correct answer.

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