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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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if p,a are the roots of x^2+2x+1=0 then quadratic equation whose roots are 1/p, 1/a Related: Equations? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about if p,a are the roots of x^2+2x+1=0 then quadratic equation whose roots are 1/p, 1/a Related: Equations? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for if p,a are the roots of x^2+2x+1=0 then quadratic equation whose roots are 1/p, 1/a Related: Equations?.
if p,a are the roots of x^2+2x+1=0 then quadratic equation whose roots are 1/p, 1/a Related: Equations? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about if p,a are the roots of x^2+2x+1=0 then quadratic equation whose roots are 1/p, 1/a Related: Equations? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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