Question

find the zeros of polynomial x cube minus 5 x square - 2 X + 24 if it is given that the product of its zeros is 12​

Answer 1

Answer:

3,4,-2

Step-by-step explanation:

f(x)=x3−5x2−2x+24f(x)=x3−5x2−2x+24

Letαβ=12Letαβ=12

α+β+γ=−(−5)=5α+β+γ=−(−5)=5

αβ+βγ+αγ=−21=−2αβ+βγ+αγ=−21=−2

αβγ=−241=−24αβγ=−241=−24

αβ=12⟹12γ=−24=γ=−2αβ=12⟹12γ=−24=γ=−2

α+β+γ=5α+β+γ=5

α+β−2=5⟹α+β=7α+β−2=5⟹α+β=7

(α−β)2=(α+β)2−4αβ=72−4×12⟹α−β=±1(α−β)2=(α+β)2−4αβ=72−4×12⟹α−β=±1

α+β=7andα−β=1α+β=7andα−β=1

(or)α+β=7andα−β=1(or)α+β=7andα−β=1

On solving we get:

α=4,β=3(or)α=3,β=4α=4,β=3(or)α=3,β=4

Hence the zeroes of the polynominal are 3, 4 and -2