Question

If alpha and beta are the roots of ac²+bx+c then find
1 I alpha + 1/ Beta.

I will Mark As branilist those who answer correct pls don't take free points.​

Answer 1

Answer :

1/α + 1/ß = -b/c

Note:

★ The possible values of the variable which satisfy the equation are called its roots or solutions .

★ A quadratic equation can have atmost two roots .

★ The general form of a quadratic equation is given as ; ax² + bx + c = 0

★ If α and ß are the roots of the quadratic equation ax² + bx + c = 0 , then ;

• Sum of roots , (α + ß) = -b/a

• Product of roots , (αß) = c/a

Solution :

Here ,

The given quadratic equation is :

ax² + bx + c = 0 .

Also ,

It is given that , α and ß are the roots of the given quadratic equation .

Thus ,

The sum of roots will be given as ;

α + ß = -b/a

Also ,

The product of roots will be given as ;

α•ß = c/a

Now ,

=> 1/α + 1/ß = (ß + α)/α•ß

=> 1/α + 1/ß = (α + ß)/α•ß

=> 1/α + 1/ß = (-b/a) / (c/a)

=> 1/α + 1/ß = (-b/a) × (a/c)

=> 1/α + 1/ß = -b/c

Hence ,

1/α + 1/ß = -b/c