If the sum of the roots of the equation ax^2 | vedclass

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(B) Let the roots of the quadratic equation $ax^2 + bx + c = 0$ be $\alpha$ and $\beta$.From the properties of quadratic equations,we have:Sum of root

Vedclass · Accepted Answer

$2ac = b(a + b)$

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(B) Let the roots of the quadratic equation $ax^2 + bx + c = 0$ be $\alpha$ and $\beta$.From the properties of quadratic equations,we have:Sum of roots: $\alpha + \beta = -\frac{b}{a}$Product of roots: $\alpha \beta = \frac{c}{a}$According to the problem,the sum of the roots is equal to the sum of the squares of the roots:$\alpha + \beta = \alpha^2 + \beta^2$We know that $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha \beta$.Substituting the values:$-\frac{b}{a} = (-\frac{b}{a})^2 - 2(\frac{c}{a})$$-\frac{b}{a} = \frac{b^2}{a^2} - \frac{2c}{a}$Multiply the entire equation by $a^2$:$-ab = b^2 - 2ac$Rearranging the terms:$2ac = b^2 + ab$$2ac = b(a + b)$

If the sum of the roots of the equation $ax^2 + bx + c = 0$ is equal to the sum of the squares of their roots,then:

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