Page No
If £ and B are the zeroes
of the quadratic polynomials P(x)=ax^2+bx+c
then evaluate
£² + B²
Share
Page No
If £ and B are the zeroes
of the quadratic polynomials P(x)=ax^2+bx+c
then evaluate
£² + B²
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
Answer:
[tex] \frac{ {b}^{2} - 2ac}{ {a}^{2} } [/tex]
Step-by-step explanation:
(£+ B)^2 = £^2 + B^2 + 2£B
=> £^2 + B^2 = (£+ B)^2 - 2£B ....... (1)
Sum of roots of a polynomial, ax^2 + bc + c = -b/a
product of roots of a polynomial = c/a
Therefore, £ + B = -b/a
and £B = c/a
On putting the values of (£+B) and £B in equation (1),
[tex] {£}^{2} + {B}^{2} = {( \frac{ - b}{a} )}^{2} - 2( \frac{c}{a} ) \\ = \frac{ {b}^{2} }{ {a}^{2} } - \frac{2c}{a} \\ = \frac{ {b}^{2} - 2ac }{ {a}^{2} } [/tex]
Please mark my answer as Brainliest!