Question

find the zeroes of the polynomial 25c^2+10c+1

Answer 1

If we want to find the zero, equation must be equal to 0,

Hence, solution :-




$25 {c}^{2} + 10c + 1 = 0 \\ \\ \\ 25 {c}^{2} + (5 + 5)c + 1 = 0 \\ \\ \\ 25 {c}^{2} + 5c + 5c + 1 = 0 \\ \\ \\ 5c(5c + 1) + 1(5c + 1) = 0 \\ \\ (5c + 1)(5c + 1) = 0 \\ \\ \\ {(5c + 1)}^{2} = 0 \\ \\ \\ 5c + 1 = 0\\ \\ \\ \boxed{ \bold{ \underline{ \: c = - \frac{ 1}{5} }}}$

Answer 2

25c2 +10c+1

product = 25 ( 5 x 5 )

sum = 10 (5+5)

25c2 + 5c +5c + 1

on factorising

5c(5c+1)+1(5c+1)

hence (5c+1)(5c+1) are the factors

now when we got the factors we can equate them to zero

so,

5c+1=0

5c=-1

c=-1/5

similarly we can find the second zero ,

second zero = -1/5