Question

Product of the zeroes of polynomial 3x²-2x-4 is ? No spam ❌ Want accurate answers ✔ No spa.

full explain​

Answer 1

`\green{ \boxed{ \bf \: product \: of \: the \: zeros \: = - (4)/(3) }}`

Explanation:

We know that,

`\sf \: if \: \alpha \: and \: \beta \: \: are \: the \: zeroes \: of \: the \: \\ \sf \: polynomial \: \: \: \pink{a {x}^(2) + bx + c }\: \: \: \: then \\ \\ \small{ \sf \: product \: of \: zeroes \: \: \: \alpha \beta = \frac{constant \: term}{coefficient \: of \: {x}^(2) } } \\ \\ \sf \implies \: \pink{ \boxed{\alpha \beta = (c)/(a) }}`

Given that, the polynomial is :

`\bf \: 3 {x}^(2) - 2x - 4`

so,

• constant term c = - 4
• coefficient of x^2 = 3

`\sf \: so \: product \: of \: zeroes \: \: = ( - 4)/(3) = - (4)/(3)`

Answer 2

9514 1404 393

Answer:

-4/3

Explanation:

Quadratic ax² +bx +c can be written in factored form as ...

a(x -p)(x -q)

for zeros p and q. The expanded form of this is ...

ax² -a(p+q)x +apq

Then the ratio of the constant term to the leading coefficient is ...

c/a = (apq)/a = pq . . . . the product of the zeros

For your quadratic, the ratio c/a is -4/3, the product of the zeros.

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Additional comment

You will notice that the sum of zeros is ...

-b/a = -(-a(p+q))/a = p+q