#MMBLTutorial
SHORTCUT#01
Double the roots, thrice the roots or n times the roots
Question: Find a quadratic equation whose roots are twice the roots of 2x² - 5x + 113 = 0.
Normally, you will solve for the roots itself via calcu or quadratic formula, then you will multiply it by 2, then solve backwards. That would be very hard if your roots became irrational.
A formula derived by Vietta, known today as Vietta's Formula enable us to solve this problem without directly solving the roots.
But Vietta's Formula would take you 20 seconds or more.
How about mentally and on the spot?
Here's how,
For any quadratic equation ax² + bx + c = 0, the corresponding equation, which is n times the roots of the given will be ax² + bnx + cn² = 0.
Syempre nakakahilo diba? Ganito lang yan.
Yung tanong natin
2x² - 5x + 113 = 0 tapos twice daw?
Ano kasama ni x? -5. Ano ung constant? 113.
Copy mo ung x² at kasama nya.
2x²
Next, yung kasama ni x, multiply mo ng 2
-5(2) = -10
Magiging
2x² - 10x na tama?
Then ung constant multiply mo sa 4. (Bakit 4? Kasi 2² = 4)
113(4) = 452
So
Sagot ay
2x² - 10x + 452 = 0
Now, simplify mo na lang
x² - 5x + 226 = 0.
ISA PA na example.
Find the quadratic equation whose roots are twenty times the roots of x² - x + 2 = 0
Sagot:
x² - 20x + 800 = 0.
20 kasi (-1)(20)
800 kasi (2)(20²)
Hope you learned guys!
-Shiro
