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(B) For a quadratic equation of the form $ax^2 + bx + c = 0$,the sum of the roots is given by $\alpha + \beta = -b/a$ and the product of the roots is

Vedclass · Accepted Answer

$7$

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(B) For a quadratic equation of the form $ax^2 + bx + c = 0$,the sum of the roots is given by $\alpha + \beta = -b/a$ and the product of the roots is given by $\alpha \beta = c/a$.Given the equation $x^2 - 3x + 1 = 0$,we have $a = 1$,$b = -3$,and $c = 1$.Thus,the sum of the roots $\alpha + \beta = -(-3)/1 = 3$ and the product of the roots $\alpha \beta = 1/1 = 1$.We need to find the sum of the squares of the roots,which is $\alpha^2 + \beta^2$.Using the identity $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha \beta$,we substitute the values:$\alpha^2 + \beta^2 = (3)^2 - 2(1) = 9 - 2 = 7$.Therefore,the sum of the squares of the roots is $7$.

What is the sum of the squares of the roots of the quadratic equation $x^2 - 3x + 1 = 0$?

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