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 $\alpha$ and $\beta$. Then,$(\alpha - \beta)^2 = (\alpha + \beta)^2 - 4\alpha\beta = a^2 - 4b$.Let the root

Vedclass · Accepted Answer

$a + b = -4$

Vedclass · Answer

(B) Let the roots of $x^2 + ax + b = 0$ be $\alpha$ and $\beta$. Then,$(\alpha - \beta)^2 = (\alpha + \beta)^2 - 4\alpha\beta = a^2 - 4b$.Let the roots of $x^2 + bx + a = 0$ be $\alpha'$ and $\beta'$. Then,$(\alpha' - \beta')^2 = (\alpha' + \beta')^2 - 4\alpha'\beta' = b^2 - 4a$.Given that the difference between the roots is equal,we have $(\alpha - \beta)^2 = (\alpha' - \beta')^2$.Therefore,$a^2 - 4b = b^2 - 4a$.Rearranging the terms,we get $a^2 - b^2 = 4b - 4a$.$(a - b)(a + b) = -4(a - b)$.Since $a 
e b$,we can divide both sides by $(a - b)$,which gives $a + b = -4$.

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 $x^2 + bx + a = 0$ $(a \ne b)$,then:

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