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Wilma and Greg were trying to solve the quadratic equation x^2 + bx + c = 0.Wilma wrote down the wrong value of b (but her value of c was correct), and found the roots to be 1 and 8. Greg wrote down the wrong value of c (but his value of b was correct), and found the roots to be 1 and -4. What are the actual roots of x^2 + bx + c = 0?

Jul 2, 2021

#1
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Start off with Wilma's equation. We can use Vieta's to find that c/a = 8*1, so c = 8.

Next Greg's equation. Using Vieta's again we can find that -b/a = -4+1 = 3

So piecing it together, the actual equation is,

$$x^2+3x+8$$

Apply quadratic formula to find the roots$$x=−1.5±\frac{\sqrt{23}i}{2}$$

Jul 2, 2021
#2
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Hey there, Guest!

Greg: (x+1)(x+4) = x^2 + 5x + 5       $$c≠5$$

Wilma: (x-1)(x-6)  =   x^2 -7x + 6.

Equation: $$(x+3)(x+2)$$

Therefore the roots are -3 & -2.

Hope this helped! :)

( ﾟдﾟ)つ Bye

Jul 3, 2021
edited by TaliaArticula  Jul 3, 2021