Question

if alpha, beta are the zeros of polynomial p(x)=x²-5 find the value of 1/alpha, 1/beta​

Answer 1

alpha and beta are the zeros of the polynomial p(x)=x2-5x+2.

x² - 5x + 2

Sum of Zeroes = -b/a

Products of Zeroes = c/a

a = 1 b = -5 c = 2

Zeroes are a & ß

a +3=5

αβ = 2

1/a + 1/3

= (B + a)/aß

= 5/2

1/αβ = 1/2

x² - 5x/2 + 1/2 = 0

=> 2x² - 5x+1=0 where zeroes are 1/a & 1/3

1/a & 1/B = (5 ± √25 - 8)/4

=

(5± √17)/4

3aß =3*2= 6

Answer 2

Answer:

Let alpha =a , beta = b

a and b are the zeroes of p(x)=x^2-5x+4 ,therefore

a+b= 5…………….(1). and. a.b= 4………………(2)

1/a+1/b-2.a.b=?

=(b+a)/a.b -2.ab. Putting a+b=5 from eqn. (1) and a.b= 4 from eqn. (2)

= 5/4 -2×4

=5/4–8

=-27/4

= -6.75. Answer.