Question

alpha and beta are the zeros of quadratic polynomial x^2 +4x+3 . then form a Polynomial whose zeros are 1+alpha/beta and 1+beta/alpha​

Answer 1

Answer:

So your question answer is => 3x²+4x+1

Step-by-step explanation:

If alpha(A) and Beta(B) are the zeroes of quadratic x²+4x+3

then,

By the properties of quadratic we can write-:

Sum of roots(A+B) = -b/a = -4. eq.1

Product of roots(AB) = c/a = 3. eq.2

Now any quadratic eq. is of form-:

=> X²-(Sum of roots)+(product of roots). eq.3

Now for a quadratic equation whose roots are 1/alpha(A) and 1/Beta(B)-:

Product of roots for new quadratic=> 1/(AB)

Sum of roots for new quadratic => (A+B)/(AB)

So, By putting values from above eq.1 and eq.2

Products of roots for new quadratic=> 1/3

&

Sum of roots for new quadratic=> -4/3

By putting values in eq.3-:

we get new quadratic eq. => X ²+(4x/3)-(1/3)

whose roots are 1/A and 1/B

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