Quadratic formula not working?

Question

Suppose I want to find the $ n $ for which

$$(n)(n+1)/2 = 10 \Longrightarrow n^2 + n - 20 = 0$$

Clearly a solution is $4$. But, suppose we wanted to find that solution by use of quadratic formula. We get

$$4 = \frac {-1 \pm \sqrt{1-80}}{2} $$

But that's clearly not true. What am I doing wrong?

$-4ac=-4(1)(-20)=-(-80)=80$. – David Mitra Dec 19 '14 at 15:14 — David Mitra, Dec 19 '14 at 15:14
That should be $\dfrac {-1 \pm \sqrt{1+80}}{2}$ – Dipanjan Pal Dec 19 '14 at 15:14 — Dipanjan Pal, Dec 19 '14 at 15:14
its $1^2-4\cdot1\cdot(-20)$=$1+80$ – Dheeraj Kumar Dec 19 '14 at 15:14 — Dheeraj Kumar, Dec 19 '14 at 15:14

score 15 · Accepted Answer · answered Dec 19 '14 at 15:13

15

You need a positive $$ \frac {-1 \pm \sqrt{1\color{green}{+}80}}{2} $$ Remember that the discriminant for $ax^2 +bx + c = 0$ is $b^2 -4ac$. Here $c = -20$. So $d = 1^2 - 4\cdot 1\cdot (-20) = 1 - (-80) = 1 + 80$.

answered Dec 19 '14 at 15:13

Thomas

43,555

score 3 · Answer 2 · answered Dec 19 '14 at 15:14

3

$$Ax^2+Bx+C=0\implies x=\frac{-B\pm\sqrt{B^2-4AC}}{2A}$$

$$\implies n=\frac{-1\pm\sqrt{1^2-4\cdot1\cdot(-20)}}{2\cdot1}$$

answered Dec 19 '14 at 15:14

lab bhattacharjee

274,582

score 2 · Answer 3 · answered Dec 19 '14 at 15:13

2

$$\frac {-1 \pm \sqrt{1+80}}{2} $$

answered Dec 19 '14 at 15:13

rlartiga

4,205
1
14
24

score 0 · Answer 4 · answered Dec 19 '14 at 15:17

0

The discriminant is : $1 - 4(-20) = 81 = 9^2$ ! Not $-79$.

answered Dec 19 '14 at 15:17

brick

1,919

score 0 · Answer 5 · edited Dec 19 '14 at 18:12

0

Let $\Delta = b^2 - 4ac$ be the discriminant. Then we see that $\Delta = (1)^2 - 4 (1)(-20)$, so $\Delta = 1 + 80 = 81$.

$$(-1) \times (-1) = 1$$

edited Dec 19 '14 at 18:12

wchargin

1,802

answered Dec 19 '14 at 15:18

Gustavo Viana

35

1

Explaining your notation might be helpful :) – Shaun Dec 19 '14 at 15:55
Delta? Never saw Delta as discriminant. – JTP - Apologise to Monica Dec 20 '14 at 02:16
2

@JoeTaxpayer Always have myself (if a symbol is used at all, anyway). – Thomas Dec 20 '14 at 03:50

Quadratic formula not working?

5 Answers5