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What calculation is modeled on the number line?
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If α and β are the Roots of a Quadratic Equation ax² + bx + c then :
✿ Sum of the Roots : α + β
✿ Product of the Roots : αβ
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
⇒ -b = 9(4)
⇒ b = -36
⇒ Product of the Roots
⇒ c = 18 × 4
⇒ c = 72
⇒ The Quadratic Equation is 4x² - 36x + 72 = 0