The quadratic equation 2x^2 + 8x + 1 = 0 has roots x1 and x2. Write down the value of x1+x2 and x1*x2 and find the value of x1^2 + x2^2

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If a quadratic equation is of the form : ax^2 +bx +c =0

and has roots x1 and x2, then the following statements are true:

x1+x2 = - b/a

x1*x2 =  c/a

In our case: x1+x2 = - 8/2 = -4

and x1*x2 = 1/2

Now, x1^2 + x2^2 = (x1+x2)^2 -2*x1*x2

= (-4)^2  -2 * 1/2 = 16 - 1 = 15

Bogdan-Adrian M. A Level Maths tutor

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