Question

p(x)=ax+b,x=-b/a Verify whether the expression is zeros of the polynomial indicated against them, or
not.

Answer 1

Hey there!

Zero of the polynomial is the value of variable for which the polynomial is zero.

Given polynomial is p(x) = ax + b

Value of x, x =
$= \frac{ - b}{a}$

Now,
$p( \frac{ - b}{a} ) = a( \frac{ - b}{a} ) + b \\ \\ \quad \quad \: \: \: \: = a( \frac{ - b} { \cancel{a}}) + b \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = - b + b \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = 0$

If x = -b/a then the polynomial is zero, So -b/a is the zero of polynomial ax+b

Answer 2

Hello student :)

Given polynomial p(x) = ax + b.

This is a linear polynomial. So it has unique solution.

Now, Let's see if -b/a would be a zero of the polynomial.

ax + b = 0
ax = -b
x = -b/a

As we know the value of the variable for which polynomial would be zero is known as zero of the polynomial. Therefore, For -b/a the given polynomial is 0

Therefore, You can conclude that -b/a is the zero of the linear polynomial ax+b.