Question

if alpha and
Beta are the two zeros of the quadratic polynomial x square - 3 x + 7 find a quadratic polynomial whose zeros are one by Alpha and one by beta

Answer 1

Solution :

The given quadratic polynomial is

f(x) = x² - 3x + 7

Since α and β are the zeroes of f(x),

• α + β = - (- 3)/1 = 3
• αβ = 7/1 = 7

We have to find the polynomial whose zeroes are 1/α and 1/β, which can be found as

g(x) = (x - 1/α) (x - 1/β)

= x² - (1/α + 1/β) x + 1/(αβ)

= x² - (α + β)x/(αβ) + 1/(αβ)

= x² - 3x/7 + 1/7

= (7x² - 3x + 1)/7

i.e., 7x² - 3x + 1