Question

Find the exact roots of 0= x^2 -7x +7

I think you have to use the quadratic formula, but I can't figure out how to do this or how to verify. If you could show me step by step, that would be awesome. Thanks

Answer 1

Every student of mathematics must know and memorize the quadratic equation formula:
for ax^2 + bx + c = 0
x = (-b ± √(b^2 - 4ac) /(2a)

for yours:
a = 1
b = -7
c = 7

x = (7 ± √(49 - 4(1)(7))/(2
= (7 ± √21)/2

x = (7 + √21)/2 OR x = (7 - √21)/2

Since it asked for the "exact" roots, you leave the answers that way.

If you are asked to "verify" , sub those values into the original equation. I will do one of the them , you try the other

if x = (7+√21)/2
LS = [(7+√21)/2]^2 - 7(7+√21)/2 + 7
= (49 + 14√21 + 21)/4 - (49 + 7√21)/2 + 7
= (70 + 14√2 - 98 - 14√21 + 28)/4
= 0/4
= 0
= RS

so x = (7 + √21)/2

You try the 2nd root.
Notice the verification looked messier than the original solving.
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