Question

If alpa and beta are the zeroes of 3x^2-4x+1find 1+(alpha/beta)and 1+(beta/alpha)

Answer 1

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1+(alpha/beta) = 4

and

1+(beta/alpha) = 4/3

step-by-step explanation:

Given,

3x^2-4x+1 = 0

it is a quadratic equation,

where,

a = 3

b = -4

c = 1

also,

the roots are 'alpha' and 'beta'

let,

alpha = m

and,

beta = n

now,

DOING factorization,

3x^2 -3x - x + 1 = 0

taking common terms,

=> 3x ( x-1) -1(x-1) = 0

=> (x-1)(3x-1) = 0

=> x = 1

and

=> x = 1/3

therefore,

m = 1

n = 1/3

now,

to Calcute,

♦ 1+(alpha/beta)

= 1+ (m/n)

= 1+ {1/(1/3)}

= 1 + 3

= 4

and,

♦1+(beta/alpha)

= 1 + (n/m)

= 1 + {(1/3)/1}

= 1+ 1/3

= (3+1)/3

= 4/3

Hence,

1+(alpha/beta) = 4

and

1+(beta/alpha) = 4/3