What is the quadratic when roots are given 13 and 3 are given ?
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The roots of the quadratic equation are 13 and 3. The quadratic equation can be written as (x - 13)(x - 3) = 0
(x - 13)(x - 3) = 0
=> x^2 - 13x - 3x + 39 = 0
=> x^2 - 16x + 39 = 0
The required quadratic equation is x^2 - 16x + 39 = 0
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The equation is written as a product of linear factors:
(x - x1)(x - x2) = 0, where x1 and x2 are the roots of the equation.
Since x1 = 13 and x2 = 3, we'll have:
(x - 13)(x - 3) = 0
We'll remove the brackets using FOIL method:
x^2 - 3x - 13x + 39 = 0
We'll combine like terms and we'll get:
x^2 - 16x + 39 = 0
The quadratic whose roots are 13 and 3 is: x^2 - 16x + 39 = 0.
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