What is the sum of the squares of the roots of $x^{2} - 5 x + 4 = 0$ $x^2-5x+4=0$ ?

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What is the sum of the squares of the roots of $x^{2} - 5 x + 4 = 0$ $x^2-5x+4=0$ ?

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Answer 1 · 2017-12-21T07:49:52

Sum of squares of roots is $17$ $17$ .

Explanation:

In an equation of the type $a x^{2} + b x + c = 0$ $ax^2+bx+c=0$ , if roots are $α$ $alpha$ and $β$ $beta$ , then sum of roots $α + β = - \frac{b}{a}$ $alpha+beta=-b/a$ and product of the roots $α β = \frac{c}{a}$ $alphabeta=c/a$ .

As the given equation is $x^{2} - 5 x + 4 = 0$ $x^2-5x+4=0$ , we have $α + β = 5$ $alpha+beta=5$ and $α β = 4$ $alphabeta=4$

As such sum of squares of roots i.e.

$α^{2} + β^{2}$ $alpha^2+beta^2$

= $α^{2} + β^{2} + 2 α β - 2 α β$ $alpha^2+beta^2+2alphabeta-2alphabeta$

= ${(α + β)}^{2} - 2 α β$ $(alpha+beta)^2-2alphabeta$

= $5^{2} - 2 \times 4$ $5^2-2xx4$

= $25 - 8$ $25-8$

= $17$ $17$

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What is the sum of the squares of the roots of $x^{2} - 5 x + 4 = 0$ $x^2-5x+4=0$ ?

1 Answer

Explanation:

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What is the sum of the squares of the roots of x2−5x+4=0x^2-5x+4=0?

1 Answer

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What is the sum of the squares of the roots of $x^{2} - 5 x + 4 = 0$ $x^2-5x+4=0$ ?