Question

If alpha and beta are the 2 zeros of the polynomial p(x)=axsquare +bx+c then alpha square +beta square is

Answer 1

p(x)=ax²+bx+c

sum of roots = -b/a

product of roots = c/a

alpha + beta = -b/a

Squaring both sides,

alpha²+beta²+2alpha beta=b²/a²

Product of roots = alpha beta = c/a

alpha²+beta²+2c/a=b²/c²

alpha²+beta²=b²/c² -2c/a