1st Problem 2016

Algebra Level 3

Find the sum of all the roots of the following equation:

$\LARGE { 4x }^{ 2} + { x } - 3 = 2$

Write the sum in the form of a simplified fraction $\frac { a }{ b }$

[If the sum is 2, write it as $\frac { 2 }{ 1 }$ ]

[If the sum is $\frac { 4 }{ 2 }$ , write it as $\frac { 2 }{ 1 }$

Write your answer as |a+b|.

Check out the set: 2016 Problems

The answer is 3.

2 solutions

Ananth Jayadev
Dec 31, 2015

Use the Vieta's Formula, where $r_1 + r_2 = -\frac {b}{a}$ . So we get $r_1 + r_2 = -\frac {1}{4}$ . That means that $-\frac {1}{4}$ is the sum of the two roots of this equation. The question stated to write the answer as $b + a$ , so the answer is $3$ as $-1 + 4 = 3$ .

$\frac{-1}{4}=\frac{1}{-4}$ .Therefore answer could be 3 or -3. The question should indeed ask |a+b|.

Rishabh Jain - 5 years, 5 months ago

I didn't think of that, thanks :D

Angela Fajardo - 5 years, 5 months ago

No problem..

Rishabh Jain - 5 years, 5 months ago

Nice Solution :)

Angela Fajardo - 5 years, 5 months ago

Thank you for the compliment!

Ananth Jayadev - 5 years, 5 months ago

Hari Om Sharma
Jun 29, 2016

Use the Vieta's Formula, where sum of the roots is -b/a. so it is -1/4. ans -1+4=3

1st Problem 2016

The answer is 3.

2 solutions

0 pending reports