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stiv31 [10]
3 years ago
13

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) 9x

2 + 36x + 35 = 0 D) 9x2 − 36x − 35 = 0
Mathematics
1 answer:
Serggg [28]3 years ago
5 0

Answer:

Option A)

9x^2 - 36x + 35 = 0

Step-by-step explanation:

We are given the following in the question:

Roots of quadratic equation are:

\alpha = \dfrac{5}{3}, \beta = \dfrac{7}{3}

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

\alpha + \beta = \dfrac{5+7}{3} = 4\\\\\alpha\beta = \dfrac{5}{3}\times \dfrac{7}{3} = \dfrac{5}{9}

Standard form of quadratic equation:

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

Putting values, we get,

x^2 - 4x + \dfrac{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

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