Question

Find the product of the zeros of the polynomial 4x3

– 7x2 + 3x – 2.​

Answer 1

Answer:

f(x)=2x

3

+6x

2

−4x+9

Let three zeroes be α,β,γ

Product of 3 zeroes=

a

−d

=

2

−9

Given Product of 2 zeroes =3

or α.β=3

⇒αβγ=

2

−9

⇒3γ=

2

−9

⇒γ=

2

−3

Third zero is

2

−3

Answer 2

Answer:

Required product is $\frac{1}{2}$

Step-by-step explanation:

Given Polynomial,

$4 {x}^{3} - 7 {x}^{2} + 3x - 2....(1)$

We want to find product of the zeroes of the given polynomial.

We know,

If $a {x}^{3} + b {x}^{2} + cx + d.....(1)$

is a polynomial then product of all zeroes of this polynomial is $( - \frac{d}{a} )$

We are comparing polynomial (1) and (2) and get

$a = 4 \\ b = - 7 \\ c = 3 \\ d = - 2$

Then product of all zeroes of Polynomial (1)

$= - ( \frac{ - 2}{4} ) \\ = \frac{2}{4} \\ = \frac{1}{2}$

This is a problem of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549

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