Question

If alpha and beta are the zeros of polynomial 3x^2+5x+13 then what will be the value of 1/alpha and 1/beta

Answer 1

Answer:

-5/13

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 ;

3x² + 5x + 13 .

Clearly,

a = 3

b = 5

c = 13

Thus,

Sum of zeros = -b/a

α + ß = -5/3

Also,

Product of zeros = c/a

αß = 13/3

Now,

1/α + 1/ß = (ß + α)/αß

= (-5/3) / (13/3)

= (-5/3)×(3/13)

= -5/13

Hence,

The required answer is : (-5/13)

Answer 2

Answer:

(-5/13)

Step-by-step explanation:

The given quadratic polynomial is;

3x^2 +5x+13

a=3

b=5

c=13

sum of zeros =-b/a

a+b=-5/3

Also,

product of zeros =c/a

ab=13/3

Now,

1/a+1/b=(b+a)/ab

(-5/3)/(13/3)

(-5/3)×(3/13)

(-5/13)

The required answer is:(-5/13)