Question

7. If a+b+c= 0, then a zero of the polynomial ax^2 + bx +c, is​

Answer 1

Answer:

1

Step-by-step explanation:

ax^2+bx+c

Let x=1

a×1+b×1+c

a+b+c

According to question

a+b+c=0

So, 1 is a zero of given polynomial.

Answer 2

Given:

A quadratic equation ax²+bx+c=0, a + b+ c =0.

To Find:

One of the roots of the above quadratic equation is?

Solution:

The given problem can be solved using the concepts of quadratic equations.

1. The given quadratic equation is  ax²+bx+c=0.

2. The relation between a, b, and c is a + b + c = 0.

3. The relation between a, b, and c can be also written as,

=> b = -(a+c),

4. Substitute the value of b in the quadratic equation,

=>  ax²+bx+c=0,

=> ax²+(-a-c)x+c=0,

=>  ax² -ax -cx + c = 0,

=> ax(x-1) -c(x-1) = 0,

=> (ax-c)(x-1) = 0,

=> The roots of the equation are x = 1, and x = (c/a).

=> Therefore, 1 is always the root of the quadratic equation for any values of a, b, and c. ( a, b, and c should satisfy the relation a+b+c=0).

Therefore, 1 is one of the zeroes of the given quadratic polynomial.