Question

Find the zeroes of the quadratic polynomial x2+6x+11, and verify the relationship between the zeroes and the coefficients.

Answer 1

Answer:

α+β=-b/a=-(-11)/6= 11/6

αβ=c/a=5/6

6x^2-11x+5=6x^2+x(-6-5)+5

6x^2-6x-5x+5

6x(x-1)-5(x-1)

(6x-5)(x-1)

6x-5=0

6x=5

x=5/6

α=5/6

x-1=0

x=1

β=1

hence α+β=5/6+1=5/6+6/6=11/6

αβ=5/6*1=5/6

hence verified