Question

Write a quadratic equation in standard form that has 5 3 and 7 3 as its roots. A) 9x2 − 36x + 35 = 0 B) 9x2 + 36x − 35 = 0 C) 9x2 + 36x + 35 = 0 D) 9x2 − 36x − 35 = 0

Answer 1

A) 9x^2 − 36x + 35 =0

Explanation:

9x^2 − 36x = −35

Using the zero-product property, write the solutions as factors of the quadratic equation and multiply:

(x − 5/3)(x − 7/3) = 0

9x2 − 36x + 35 = 0

9x2 − 36x = −35

Answer 2

Option A)

`9x^2 - 36x + 35 = 0`

Explanation:

We are given the following in the question:

Roots of quadratic equation are:

`\alpha = (5)/(3), \beta = (7)/(3)`

The sum of the roots and the product of the roots can be calculated as:

`\alpha + \beta = (5+7)/(3) = 4\\\\\alpha\beta = (5)/(3)* (7)/(3) = (5)/(9)`

Standard form of quadratic equation:

`x^2-(\alpha + \beta)x+\alpha\beta = 0`

Putting values, we get,

`x^2 - 4x + (35)/(9) = 0\\\\9x^2 - 36x + 35 = 0`

is the required quadratic equation.

Thus, the correct answer is

Option A)

`9x^2 - 36x + 35 = 0`