If alpha and beta are the zeros of the polynomial 3x^2-4x+2, then which polynomial represents the polynomial whose zeroes are - Maths - Polynomials

Question

If alpha and beta are the zeros of the polynomial 3x^2-4x+2, then
which polynomial represents the polynomial whose zeroes are
(1/alpha) and (1/beta)?

Kavita Verma · Accepted Answer

Dear Student,

Let 3x2 - 4x + 2 = 0zeros = α, βSum of zeros = -ba⇒ α + β = -(-4)3 = 43product of zeros = ca ⇒ α×β = 23Now let the second equation is ax2 + bx + c = 0roots = 1α, 1βSum of zeros = -ba⇒1α + 1β= α + βαβ =  4323 = 2 = -ba⇒ b = -2aproduct of zeros = ca ⇒ 1α × 1β = 32 = ca   
 as α×β = 23⇒ 3a = 2c ⇒ c = 3a2Putting all the values back, we get,ax2 + bx + c = 0⇒ ax2 + -2ax + 3a2 = 0⇒a22x2 - 4x + 3 = 0⇒ 2x2 - 4x + 3 = 0
So, the required polynomial is 2x2 - 4x + 3
Regards,

If alpha and beta are the zeros of the polynomial 3x^2-4x+2, then which polynomial represents the polynomial whose zeroes are (1/alpha) and (1/beta)?