Question

if the root of equation is x²-14x+48=0 are in AP. The smaller the root is first term of AP find sum of 12 terms​

Answer 1

Step-by-step explanation:

x²-14x+48=0

x²-6x -8x+48=0

x(x-6)-8(x-6)=0

(x-6)(x-8)=0

x-6=0. x-8=0

x=6. x=8

By condition ,the smaller the root is first term of A.P. hence,6 is the first term of A.P.

a=6

Now 8 is the second term of AP

a2=8

Now,a2-a1=d

8-6=d

d=2

Sn=n/2(2a +(n-1)d)

S12=12/2(2×6+(12-1)2)

=6(12+11×2)

=6(12+22)

=6(34)

=204

Thus,the sum of 12 terms is 204