Question

(4) Write the sum and the product of the roots of 2x + 10x - 5 = 0.​

Answer 1

Step-by-step explanation:

a=2,b=10,c=-5

the roots=-b±√b²-4ac/2a

=-10±√10²-4×2×-5/2×2

=-10±√100+40/4

=-10±√140/4

=-10±√4×35/4

=-10±2√35/4

=2(-5±√35)/4

=-5±√35/2

so the roots are alpha=-5+√35/2,beta=-5-√35/2

sum of the roots=-5+√35/2+(-5-√35/2)

=-5+√35-5-√35/2

=-10/2

=-5

product of roots=(-5+√35/2)(-5-√35/2)

=(-5)²-(√35)²/4

=25-35/4

=-10/4=-5/2

otherwise we can do by short cut

alpha + beta=-b/a=-10/2=-5

alpha×beta=c/a=-5/2