Question

If $\alpha,\beta$ are the zeros of a polynomial $2y^{2}+7y+5$, write the value of $\alpha+\beta + \alpha\beta$

Answer 1

SOLUTION :

Given : α  and β are the zeroes of the  polynomial f(y) = 2y² + 7y +5  

On comparing with ay² + by + c,

a = 2 , b= 7, c = 5

Sum of the zeroes = −coefficient of y / coefficient of y²

α + β  = -b/a = -7/2

α + β  = -7/2

Product of the zeroes = constant term/ Coefficient of y²

αβ = c/a = 5/2

αβ = 5/2

The value of α +  β + αβ :  

= -7/2 + 5/2  

= (-7+5)/2

= -2/2

= -1

Hence, the value of α +  β + αβ is -1.

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Answer 2

Hi there!
Here's the answer:

•°•°•°•°•°<><><<><>><><>°•°•°•°•°•°

For a quadratic equation $ax^{2}+bx+c=0$

•Sum of roots = $-\frac{b}{a}$
• Product of roots = $\frac{c}{a}$

•°•°•°•°•°<><><<><>><><>°•°•°•°•°•°

¶¶¶ SOLUTION:

Given,
Polynomial f(y) = $2y^{2}+7y+5$

And $\alpha,\beta$ are ita zeros(or roots)

¶ Find Sum of roots to get $\alpha+\beta$

=> $\alpha+\beta$ = $-\frac{7}{2}$-----[1]

¶ Find Product of roots to get $\alpha\beta$

=> $\alpha+\beta$ = $\frac{5}{2}$------[2]

¶ Find $\alpha+\beta+\alpha\beta$
Add [1]&[2]

$\alpha+\beta+\alpha\beta = -\frac{7}{2}+\frac{5}{2}$

=> $\alpha+\beta+\alpha\beta = \frac{-7+5}{2}$

=> $\alpha+\beta+\alpha\beta = -1$

•°•°•°•°•°<><><<><>><><>°•°•°•°•°•°

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