Question

If alpha and beta are the zeroes of polynomial 2x^2+7x+5 then write the value of alpha+beta+(alpha)(beta)

Answer 1

Answer:

see the attachment for answer

Step-by-step explanation:

so your final answer is-

-1.

I hope you get the right answer

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Answer 2

Answer:

α + ß + αß = -1

Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros .

★ A quadratic polynomial can have atmost two zeros .

★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ;

• Sum of zeros , (α + ß) = -b/a

• Product of zeros , (αß) = c/a

Solution:

Here,

The given quadratic polynomial is ;

2x² + 7x + 5 .

On comparing the given quadratic polynomial with the general form ax² + bx + c ,

We have ;

a = 2

b = 7

c = 5

Also,

It is given that , α and ß are the zeros of the given quadratic polynomial .

Thus,

=> Sum of zeros = -b/a

=> α + ß = -7/2

Also,

=> Product of zeros = c/a

=> αß = 5/2

Now,

α + ß + αß = (α + ß) + αß

= -7/2 + 5/2

= (-7 + 5)/2

= -2/2

= -1

Hence,

α + ß + αß = -1