Question

If two zeroes of a polynomial x^3+5x^2+7x+3 are -1 and -3 ,then find the third zero

Answer 1

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Answer 2

Answer:

Third zero (ɣ) = -1

Step-by-step explanation:

Given that :

• Two zeroes of the polynomial (ɑ & β) are -1 and -3.

Now we know, if ɑ, β and ɣ are the zeroes of the cubic polynomial p(x) = x³ + 5x² + 7x + 3, then

• ɑ + β + ɣ = -b/a

• ɑβ + βɣ + ɣɑ = c/a

• ɑ.β.ɣ = -d/a

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In our case,

☛ ɑ = -1

☛ β = -3

☛ ɣ = ?

∴ Using the formula, we get,

☛ ɑ + β + ɣ = -5/1

☛ -1 + -3 + ɣ = -5

☛ ɣ - 4 = -5

☛ ɣ = -1

∴ The third zero if the polynomial (ɣ) is -1