Question

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

full explain​

Answer 1

9514 1404 393

Answer:

  -4/3

Step-by-step 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

Answer 2

Answer:

$\green{ \boxed{ \bf \: product \: of \: the \: zeros \: = - \frac{4}{3} }}$

Step-by-step explanation:

We know that,

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

Given that, the polynomial is :

$\bf \: 3 {x}^{2} - 2x - 4$

so,

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

$\sf \: so \: product \: of \: zeroes \: \: = \frac{ - 4}{3} = - \frac{4}{3}$