Question

if x²+ 3 x - 2 =0 and alpha and beta are the zeros of it find 1/ alpha + 1 /beta ​

Answer 1

$\Large{\underline{\underline{\mathfrak{\tt{\red{Solution}}}}}}$

$\Large{\underline{\underline{\mathfrak{\tt{\pink{Given}}}}}}$

• equation be , x² + 3x - 2 = 0 ________(1)
• α & β are zeroes of this equation.

$\Large{\underline{\underline{\mathfrak{\tt{\pink{Find}}}}}}$

• Value of 1/α + 1/β

$\Large{\underline{\underline{\mathfrak{\tt{\red{Explanation}}}}}}$

We Know,

★ Sum of zeroes = -(coefficient of x)/(coefficient of x²)

★product of zeroes = (constant part)/(coefficient of x²)

So, now

➛ Sum of zeroes = -(3)/(1)

➛ α + β = -3 _________________(2)

Now, again.

➛product of zeroes = -2

➛α . β = -2______________(3)

Now, calculate

➛1/α + 1/β = (α + β)/(α . β)

Keep Value by equ(1) & equ(2)

➛1/α + 1/β = -3/(-2)

➛1/α + 1/β = 3/2

$\Large{\underline{\underline{\mathfrak{\tt{\red{Hence}}}}}}$

• Value of 1/α + 1/β be = 3.

_______________________

Answer 2

We Know,

★ Sum of zeroes = -(coefficient of x)/(coefficient of x²)

★product of zeroes = (constant part)/(coefficient of x²)

So, now

➛ Sum of zeroes = -(3)/(1)

➛ α + β = -3 _________________(2)

Now, again.

➛product of zeroes = -2

➛α . β = -2______________(3)

Now, calculate

➛1/α + 1/β = (α + β)/(α . β)

Keep Value by equ(1) & equ(2)

➛1/α + 1/β = -3/(-2)

➛1/α + 1/β = 3/2

Hence,

Value of 1/α + 1/β be = 3.