Question

If alpha,beta are the zeroes of the polynomial x² +x+1 then find the value of $\frac{1}{\alpha } +\frac{1}{\beta }$.

Answer 1

⭐Solution⭐

✏Given equations ,

↪X² + X +1 =0.......(1)

[ let alpha = a , beta =b ]

So,

♠ Sum of zeroes = -(coff. of x )/(coff. of x²)

a+b = -1/1

=> a+b = -1......(2)

♠

Product of zeros = (constant part )/(coff. of x²)

ab = 1/1

=>ab = 1...........(1)

But,

1/a + 1/b

= (a+b)/ab

[ keep value by (2) and (3) ]

= (-1)/1

= -1

✏Hopes ita helps u.

@Abhi❤❤

Answer 2

SOLUTION:-

Given:

·If alpha, beta are the zeroes of the polynomial x² +x +1.

To find:

The value of $\frac{1}{\alpha } +\frac{1}{\beta }$.

Explanation:

We have,

x² + x+ 1

• A=1
• B=1
• C=1

Sum of the zeroes of the quadratic polynomial:

$\alpha +\beta =\frac{-b}{a} \\\\\alpha +\beta=\frac{-1}{1} \\\\\alpha +\beta =-1$

&

Product of zeroes of the quadratic polynomial:

$\alpha \beta =\frac{c}{a} \\\\\alpha \beta =\frac{1}{1} \\\\\alpha \beta =1$

Now,

$\frac{1}{\alpha } +\frac{1}{\beta } \\\\\frac{\alpha+\beta  }{\alpha \beta } \\\\\frac{-1}{1} =-1$

Thus,

the value of 1/alpha +1/beta =-1