Question

if alpha and beta are the zeroes of x^2+5x+6 find the value of alpha^-1 + beta^-1 pls answer new don't give already given answers
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Answer 1

Answer:

– 5/6

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 :

x² + 5x + 6 .

Clearly,

a = 1

b = 5

c = 6

Also,

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

Thus,

Sum of zeros = -b/a

α + ß = -5/1 = -5

Also,

Product of zeros = c/a

αß = 6/1 = 6

Now,

α^(-1) + ß^(-1) = 1/α + 1/ß

= (ß + α) / αß

= (α + ß) / αß

= -5/6

Hence,

The required answer is (-5/6) .