Question

if alpha and beta are zeros of PX is equal to X square + X - 1 then find one upon alpha plus one upon beta​

Answer 1

Answer:

Step-by-step explanation:

Given: α and β are zeros of polynomial x²+x-1.

Therefore, p(x)=x²+x-1

a=1 b=1 c=-1

Since, α and β are zeros of p(x).

Therefore, sum of zeros => α+β=-b/a

=-1/1

=1

product of zeros =>αβ=c/a

=-1/1

=1

Now, to find ¹/α+¹/β

▪¹/α+¹/β

▪β+α/αβ [lcm of α and β is αβ]

=-1/-1

=1

Therefore, ¹/α+¹/β=1.

Answer 2

Answer:

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

Step-by-step explanation:

Explanation:

Given in the question that, P(x) = $x^2 + x -1$.

And $\alpha \ and \ \beta$ are the zeroes of the polynomial.

Step 1:

As we know that sum of zeroes of the polynomial($\alpha +\beta$) = $\frac{-b}{a}$ = -1

and product of zeroes  $\alpha \beta$ = $\frac{c}{a}$ = -1

Where a , b and c are the coefficient of $x^2$ , x and the constant value.

Now, according to the question we need to find out the value of $\frac{1}{\alpha } + \frac{1}{\beta }$.

 ⇒ $\frac{1}{\alpha } + \frac{1}{\beta }$

⇒ $\frac{\beta + \alpha }{\alpha \beta }$  ......(i)

On putting the value of ($\alpha \beta$) and ($\alpha + \beta$)  in (i) we get

⇒ $\frac{-1}{-1}$ = 1

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

Final answer:

Hence, the value of $\frac{1}{\alpha } + \frac{1}{\beta }$ is 1.

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