If #x^2-10ax-11b=0# and #x^2-10cx-11d=0# then what is # a+b +c+d#?
3 Answers
Explanation:
The sum of roots of a quadratic equation is easily given as
For the first equation:
For the second:
Thus
To learn more, look up Vieta's Formulas.
Explanation:
If we have a quadratic equation
Hencce as
Further as
Hence
# a+b +c+d= 10a+10c #
Explanation:
There is a relationship between the roots of a quadratic equation and the coefficients:
If the quadratic equation:
# ax^2 + bx + c = 0 #
Has roots
# alpha + beta = -b/a# , and#alpha \ beta = c/a #
So for the first equation
# c+d = -(10a)/1 = 10a #
Similarly, for the second equation
# a+b = -(10c)/1 = 10c #
And adding these two results we get:
# a+b +c+d= 10a+10c #