Question

If alpha and beta are the zeros of the quadratic polynomial x2+x-2 find the value of 1/alpha-1/beta

Answer 1

Answer:

Zeros Of Polynomial Below :

x²+x-2=0

x²+2x-x-2=0

x(x+2)-1(x+2)=0

(x-1)(x+2)=0

So x=1      

   x=-2

So α=1,β=-2

1/α=1

1/β=-1/2

We know that:

x²-(sum of zeros)x+(product of zeros)

so quad. eq. will be

x²-(1+-1/2)x+(1*-1/2)

x²-1/2x-1/2

and simply

2x²-x-1

HENCE SOLVED

Answer 2

Given quadratic polynomial is

${x}^{2} + x - 2 = 0$

Quadratic equation contains two roots

Let the roots are

$\alpha \: and \: \beta$

let's solve the given quadratic equation

${x}^{2} + x - 2 = 0 \\ {x}^{2} + 2x - x - 2 = 0 \\ x(x + 2) - 1(x + 2) = 0 \\ (x - 1)(x - 2) = 0 \\ x = 1 \: or \: 2$

Let

$\alpha = 1 \\ \beta = 2$

Now we need to find the value of

$(1 \div \alpha) - (1 \div \beta ) \\ 1 \div 1 - 1 \div 2 \\ 1 - 1 \div 2 \\ 1 \div 2$

Therefore, the value of

$1 \div \alpha - 1 \div \beta = 1 \div 2$

#SPJ2