Question

If α and β are the zeroes of the polynomial x2 – 19 x + 60 then 1/α + 1/β is

Answer 1

Step-by-step explanation:

x²-19x+60

x²-15x-4x+60

x(x-15)-4(x-15)

(x-4)(x-15) then roots a=4, b=15

1/4 +1/15

=15+4/60=19/60

Answer 2

Answer:

$\frac{19}{60}$

Step-by-step explanation:

Polynomial given:

$x^{2} -19x+60=0$

We know, in quadratic polynomial,

• α+β = $\frac{-b}{a}$

• α×β = $\frac{c}{a}$

where α and β are roots of the equation.

Now, α+β = $\frac{-(-19)}{1}$ = 19     -(i)

and α×β = $\frac{60}{1}$ = 60      -(ii)

Now, $\frac{1}{\alpha } + \frac{1}{\beta } =\frac{\beta +\alpha }{\alpha \beta }$

Put values of (i) and (ii):

=$\frac{19}{60}$, which is your required answer.

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