Question

if alpha and beta are zeroes of x(square) - 4x + 3. then find a quadratic polynomial whose zeroes are 1/ alpha and 1/ beta

Answer 1

Hey!

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Let @ be alpha and ß be beta .

Now,

f (x) = x^2 - 4x + 3

a = 1
b = -4
c = 3

@ and ß are zeroes of f (x)

We know,

Sum of zeroes = -b/a

@ + ß = -b/a
= - (-4) / 1
= 4

Product of zeroes = c/a

@ß = c/a
= 3/1
= 3

We need to find a quadratic polynomial whose zeroes are 1/@ and 1/ß

Sum of zeroes = 1/@ + 1/ß
= @ + ß / @ß
= 4/3

Product of zeroes = 1/@ × 1/ß
= 1 / @ß
=1/3

We know,

Quadratic polynomial =
x^2 - ( @ + ß) x + (@ß)

= x^2 - (4/3) x + (1/3)

= x^2 - 4/3 x + 1/3

That's all!

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Hope it helps...!!!

Answer 2

See the pic and ask if there is any doubt.