Question

If alfa and beta are zeroes of the polynomial 3x² + 2x+6, find the value of: a) alfa - beta

Answer 1

hii dear!!
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its similar like that:

☆☆.x2 + 2x - 6Comparing this polynomial with standard polynomial ax2 + bx + c,

▪we get,a = 3 , b= 2 and c =-6

▪Since, α & β are the zeroes of the given polynomial 3x2 + 2x - 6,

▪ then,α + β = -ba = -23And αβ = ca = -63 = -21

▪We know that α - β2 = α+ β2 - 4 αβ⇒ α - β2 = -232 - 4 × -2⇒α - β2 = 49 +8⇒α - β2 = 4 + 729 = 769

▪Therefore, α - β = 763 =4 × 193 = 2193 2

▪We know that α + β2 = α2 + β2 + 2 αβ⇒ -232 = α2 + β2 + 2 -2⇒ 49 = α2 + β2 - 4⇒ 49 + 4 = α2 + β2⇒ 4 + 369 = α2 + β2⇒ α2 + β2 = 4093

▪We know that α + β3 = α3 + β3 + 3 αβ α + β⇒ -233 = α3 + β3 + 3 -2 -23⇒ -827 = α3 + β3 + 4⇒ -827- 4 = α3 + β3⇒ -8 - 10827 = α3 + β3⇒ α3 + β3 = -116274 1α + 1β= β + ααβ = α + βαβ = -23-21 = -23 × -12 = 13...
__________________________________________hope help u