Without finding the roots of the equation 2x^2−5x+1=0, find the difference of squares of the roots.

(5/4)√17

Step-by-step explanation:

You can use the roots given by the quadratic formula and find the difference of their squares.

x1 = (-b +√( ))/(2a) . . . . . one of the two roots

x2 = (-b -√( ))/(2a) . . . . . the other root

We'll use the fact that a^2-b^2 = (a+b)(a-b) to find the difference of the squares of the roots.

x1+x2 = -b/a

x1-x2 = √( )/a

And the product of these is ...

x1^2 -x2^2 = (x1+x2)(x1-x2) = -b√(b^2 -4ac)/a^2

For the given quadratic, this difference is ...

= -(-5)/(2^2)·√((-5)^2 -4(2)(1)) = (5/4)√17

5 x 14?

im new, sorry if this is wrong.

step-by-step explanation: