Question

alpha amd beta  are zeroes of x2+2x-1, then find 1\alpha+1\beta​

Answer 1

Given:

• α and β are the zeroes of x²+2x-1

To Find:

• The Value if 1/α +1/β.

Answer:

Let us first simplify 1/α +1/β.

⇒1/α +1/β.

⇒α + β / α β.

We can now see that in numerator sum of roots is there and in denominator product of roots is there.

So , of a quadratic equation of standard form ax²+bx + c = 0 .

• Sum of roots is given by -b/a.
• Product of roots is given by c/a.

⇒-b/a = -2/1 = -2.

⇒c/a = -1/1 = -1.

On putting the respective values,

⇒1/α +1/β = α + β / α β..

⇒1/α +1/β = -2/-1.

⇒1/α +1/β = 2.

Hence the required answer is 2.