If α and β are the roots of the equation ax2 + bx + c = 0, then α / [ɑβ + b] + β / [aɑ + b] =

A quadratic equation is an equation of degree 2, meaning that the highest exponent of this function is 2.

The standard form of a quadratic is y = ax2 + bx + c,

where a, b, and c are numbered and a cannot be 0.

Examples of quadratic equations include all of these:

  • y = x2 + 3x + 1
  • y = x2

Sum and Product of roots:

If α and β are the roots of a quadratic equation, then

  • S = α+β= -b/a = coefficient of x/coefficient of x2
  • P = αβ = c/a = constant term/coefficient of x2

Solution

 The given equation is ax² + bx + c = 0

It is given that α and β are the roots of the equation ax2 + bx + c = 0.

2 + bɑ + c = 0

aɑ + b = – c / ɑ

ɑβ2 + bβ + c = 0

(ɑβ + b) = – c / β

α / [ɑβ + b] + β / [aɑ + b] = (ɑβ / – c) + (ɑβ / – c) = – 2ɑβ / c

= – 2 / a

Check out the video given below to know more about quadratic equations

Further Reading
  1. What is a quadratic equation? How can you solve a quadratic equation by the factorization method?
  2. What is an algebraic expression?

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