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  • Difference between the corresponding roots of <img alt="x^2 + ax + b = 0 \:\:\:and \:\:x^2 + bx + a = 0" src="https://entrancecorner.oncodecogs.com/gif.latex?x%5E2%20&plus;%20ax%20&plu

Difference between the corresponding roots of x^2 + ax + b = 0 \:\:\:and \:\:x^2 + bx + a = 0  is same and a ≠ b, then

Option: 1

a + b + 4 = 0


Option: 2

a + b - 4 = 0


Option: 3

a - b - 4 = 0


Option: 4

a - b + 4 = 0


Answers (1)

best_answer

Roots of the quadratic equation  x^2 + ax + b = 0 are 

\alpha=\frac{-b+\sqrt{b^2-4a}}{2},\;\;\beta=\frac{-b-\sqrt{b^2-4a}}{2}

and, roots of the quadratic equation  x^2 + bx + a = 0 are

\gamma=\frac{-a+\sqrt{a^2-4b}}{2},\;\;\delta=\frac{-a-\sqrt{a^2-4b}}{2}

Given that

\alpha-\beta=\gamma-\delta

\\\Rightarrow b^2-4a=a^2-4b\\\Rightarrow b^2-a^2+4b-4a=0\\\Rightarrow (b-a)(b+a)+4(b-a)=0\\\Rightarrow b+a+4=0

Posted by

avinash.dongre

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