Question

If α and β are the roots of the quadratic equation x²- 2x - 7= 0, find the value α² + β².

Answer 1

HOLA

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$x {}^{2} \: - \: 2x \: - \: 7 \\ \\ \\ ( \alpha \: + \: \beta ) \: = \: \frac{ - \: b}{a} = \: \frac{ - 2}{1} \\ \\ ( \alpha \: + \: \beta ) {}^{2} \: = \: ( \frac{ - 2}{1} ) {}^{2} \: = \: \frac{ - 4}{1}$

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Answer 2

If α and β are the roots of the quadratic equation x²- 2x - 7= 0, find the value α² + β².

Answer :

The given equation is : x² - 2x - 7= 0

Here,

If we compare the given equation with ax² + bx + c = 0, we get

a = 1

b = -2

c = -7

Now,

If α and β are the roots of quadratic equation ax² + bx + c = 0, then

α + β = -b/a  and    αβ = c/a

α + β = -b/a = -2/1 = -2

αβ = c/a = -7/1 = -7

Thus,

α² + β² = (α + β) - 2αβ

= (2)²  - 2 (-7)

= 4 - 14

= -18

Hence,

α² + β² = (-18)