Question

if alpha and beta are the zeros of the polynomial 3xsqaure-5x-9 find the value of 2/alpha+2/beta

Answer 1

Step-by-step explanation:

Given :-

α and β are the zeores of the polynomial

3x^2 -5x-9 .

To find:-

Find the value of (2/α)+(2/β) ?

Solution:-

Given quardratic polynomial is 3x^2 -5x-9

P(x) = 3x^2 -5x-9

On Comparing this with the standard quadratic polynomial ax^2+bx+c

a = 3

b = -5

c = -9

We know that

Sum of the zeores = -b/a

α + β = -(-5)/3

α + β = 5/3---------------(1)

Product of the zeroes = c/a

α β = -9/3

α β = -3 ------------------(2)

Now the value of (2/α)+(2/β)

=> 2[(1/α)+(1/β)]

=>2[(α + β)/α β ]

=> 2[(5/3)/(-3)]

=> 2[5/(3×-3)]

=> 2[5/-9]

=> 2(-5/9)

=> (2×-5)/9

=> -10/9

Answer:-

The value of (2/α)+(2/β) for the given problem is -10/9

Used formulae:-

• The standard quadratic polynomial ax^2+bx+c

• Sum of the zeores = -b/a

• Product of the zeroes = c/a