Question

In the equation 3x2 + 4x + (2k - 5)= 0 find k if the product of the root is 10

Answer 1

Answer:

Product of roots =(2k-5)/3=10

2k-5=30

2k=35

K=35/2

Answer 2

Answer:

Required value of k is $17 \frac{1}{2}$

Step-by-step explanation:

Given equation is

$3 {x}^{2} + 4x + (2k - 5) = 0...(1)$

We are comparing equation

$a {x}^{2} + bx + c = 0$

with equation (1) and get,

$a = 3 \\ b = 4 \\ c = 2k - 5$

We know if equation

$a {x}^{2} + bx + c = 0$

has two roots then product of their roots will be $\frac{c}{a}$

So, product of roots of equation (1) is $(\frac{2k - 5}{3} )$

According to question,

$(\frac{2k - 5}{3} ) = 10 \\ 2k - 5 = 3 \times 10 \\ 2k - 5 = 30 \\ 2k = 30 + 5 \\ 2k = 35 \\ k = \frac{35}{2} \\ k = 17 \frac{1}{2}$

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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