Question

Page No
If £ and B are the zeroes
of the quadratic polynomials P(x)=ax^2+bx+c
then evaluate
£² + B²​

Answer 1

Answer:

$\frac{ {b}^{2} - 2ac}{ {a}^{2} }$

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),

${£}^{2} + {B}^{2} = {( \frac{ - b}{a} )}^{2} - 2( \frac{c}{a} ) \\ = \frac{ {b}^{2} }{ {a}^{2} } - \frac{2c}{a} \\ = \frac{ {b}^{2} - 2ac }{ {a}^{2} }$

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