DERIVATION OF A FORMULA
Asked by | 10th Apr, 2008, 04:32: PM
if α ,β , γ are the 3 zeros of a cubic polynomial ax³ +bx² + cx +d and a not equal to 0.
then, α+β +γ = - b/a , (coefficient of x² / coefficient of x³) , α β + β γ + γ α= -c/a (coefficient of x / coefficient of x³) , and αβγ = - d/a ( constant term / coefficient of x³)
Example: 3 , -1 , -1/3 are the zeros of 3x³ -5x² - 11x - 3 so we take α = 3 , β =- 1 and γ = - 1/3
α + β +γ = 3 + (-1) + (- 1/3) = - (-5)/ 3 = -b/ a
αβ + βγ + γα = 3x ( -1) + (-1) x (-1/3) + n(-1/3) x 3 = -11/3 = c/a.
αβγ =3 x(-1) x(-1/3) =1 = -(-3)/3 = -d /a
Answered by | 17th Apr, 2008, 11:45: PM
Kindly Sign up for a personalised experience
- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions
Verify mobile number
Enter the OTP sent to your number