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if p,a are the roots of x^2+2x+1=0 then quadratic equation whose roots are 1/p, 1/a
? Related: Equations
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if p,a are the roots of x^2+2x+1=0 then quadratic equation whose roots...
Quadratic Equation with Roots 1/p and 1/a
To find the quadratic equation whose roots are 1/p and 1/a, we can use the following method:
1. Find the sum and product of 1/p and 1/a.
The sum of 1/p and 1/a is (1/p) + (1/a) = (a + p)/ap, and the product is (1/p)(1/a) = 1/(pa).
2. Use the sum and product to form the quadratic equation.
Since the roots of the quadratic equation are 1/p and 1/a, we can write the equation in the form:
(x - 1/p)(x - 1/a) = 0
Expanding the brackets gives:
x^2 - (1/p + 1/a)x + 1/(pa) = 0
Substituting the values of the sum and product from step 1 gives:
x^2 - [(a + p)/ap]x + 1/(pa) = 0
Simplifying the equation gives:
x^2 - (a + p)x + 1 = 0
Therefore, the quadratic equation whose roots are 1/p and 1/a is:
x^2 - (a + p)x + 1 = 0.
To find the quadratic equation whose roots are 1/p and 1/a, we can use the following method:
1. Find the sum and product of 1/p and 1/a.
The sum of 1/p and 1/a is (1/p) + (1/a) = (a + p)/ap, and the product is (1/p)(1/a) = 1/(pa).
2. Use the sum and product to form the quadratic equation.
Since the roots of the quadratic equation are 1/p and 1/a, we can write the equation in the form:
(x - 1/p)(x - 1/a) = 0
Expanding the brackets gives:
x^2 - (1/p + 1/a)x + 1/(pa) = 0
Substituting the values of the sum and product from step 1 gives:
x^2 - [(a + p)/ap]x + 1/(pa) = 0
Simplifying the equation gives:
x^2 - (a + p)x + 1 = 0
Therefore, the quadratic equation whose roots are 1/p and 1/a is:
x^2 - (a + p)x + 1 = 0.
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if p,a are the roots of x^2+2x+1=0 then quadratic equation whose roots are 1/p, 1/a Related: Equations?
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