Question

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If one of the zeroes of the cubic polynomial x3 + ax² + bx + c is -1, then the product of the other two zeroes is

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Answer 1

Answer:

(1 - a + b)

Step-by-step explanation:

Given Cubic Equation → x³ + ax² + bx + c

Since -1 is given as a factor of this expression, substitute x as -1 and equate it to 0. This is known as the "Factor theorem."

   p(x) = x³ + ax² + bx + c

⇒ p(-1) = (-1)³ + a(-1)² + b(-1) + c = 0

⇒ p(-1) = -1 + a - b + c = 0

⇒ a - b + c = 1

⇒ c = 1 - a + b     ----- [Equation ①]

Now,

Product of Zeroes = -(constant) ÷ x³ coefficient

Let the 3 zeroes be α, β, γ.

⇒ αβγ = -c ÷ 1

⇒ αβγ = -c

It is already given in the question that -1 is a zero.

So, let α = -1

αβγ = -c

⇒ -1 (βγ) = -c

⇒ βγ = c

So, the product of other 2 zeroes = c.

From Equation 1 we know that;

c = 1 - a + b

∴ The product of the other two zeroes is:

(1 - a + b)

Answer 2

Step-by-step explanation:

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♧♧Answered by Rohith kumar maths dude :-

I posted your answers in attachment refer it

♧♧Hope it helps u mate .

♧♧Thank you .