If the difference between the roots of the eq | vedclass

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Question

(B) Let the roots of $x^2 + ax + b = 0$ be $\alpha, \beta$ and the roots of $x^2 + bx + a = 0$ be $\alpha', \beta'$.Given that $|\alpha - \beta| = |\a

Vedclass · Accepted Answer

$a + b = -4$

Vedclass · Answer

(B) Let the roots of $x^2 + ax + b = 0$ be $\alpha, \beta$ and the roots of $x^2 + bx + a = 0$ be $\alpha', \beta'$.Given that $|\alpha - \beta| = |\alpha' - \beta'|$.Squaring both sides,we get $(\alpha - \beta)^2 = (\alpha' - \beta')^2$.Using the identity $(\alpha - \beta)^2 = (\alpha + \beta)^2 - 4\alpha\beta$,we have:$a^2 - 4b = b^2 - 4a$.Rearranging the terms,we get $a^2 - b^2 = 4b - 4a$.$(a - b)(a + b) = -4(a - b)$.Since $a 
eq b$,we can divide both sides by $(a - b)$:$a + b = -4$.

If the difference between the roots of the equation $x^2 + ax + b = 0$ is equal to the difference between the roots of the equation $x^2 + bx + a = 0$ $(a \neq b)$,then:

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