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san4es73 [151]
3 years ago
5

Write the quadratic equation whose roots are 6 and 3, and whose leading coefficient is 4

Mathematics
1 answer:
nekit [7.7K]3 years ago
8 0

If α and β are the Roots of a Quadratic Equation ax² + bx + c then :

✿  Sum of the Roots : α + β \mathsf{= \frac{-b}{a}}

✿  Product of the Roots : αβ \mathsf{= \frac{c}{a}}

Let the Quadratic Equation we need to find be : ax² + bx + c = 0

Given : The Roots of a Quadratic Equation are 6 and 3

⇒ α = 6 and β = 3

Given : The Leading Coefficient of the Quadratic Equation is 4

Leading Coefficient is the Coefficient written beside the Variable with Highest Degree. In a Quadratic Equation, Highest Degree is 2

Leading Coefficient of our Quadratic Equation is (a)

⇒ a = 4

⇒ Sum of the Roots \mathsf{: (6 + 3) = \frac{-b}{4}}

⇒ -b = 9(4)

⇒ b = -36

⇒ Product of the Roots \mathsf{: (6 \times 3) = \frac{c}{4}}

⇒ c = 18 × 4

⇒ c = 72

⇒ The Quadratic Equation is 4x² - 36x + 72 = 0

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To determine the minimum cost:

We have to determine the minimum cost of producing this product.

Since f(x) = 5x^{2} -70x+258.

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Dividing the above equation by 5, we get

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So, adding and subtracting from the above equation.

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Now, let f'(x)=0

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