Question

there is a quadratic ax^2 + bx + c where a,b,c are real numbers and a+b+c = 0 can u guess a solution of the eqation ax^2 + bx + c =0

Answer 1

Topic :-

Quadratic Equation

Given :-

There is a quadratic polynomial :

• ax² + bx + c

where

• a, b and c are real numbers
• a + b + c = 0

To Find :-

Possible roots of quadratic equation :

• ax² + bx + c = 0

Solution :-

We are provided with a quadratic polynomial and a condition for coefficients of its terms. With the help of given condition we will find the roots of the required equation.

We know that if any number satisfies the equation then it is known as root of the equation.

Given quadratic equation :

ax² + bx + c = 0

Checking value of given equation at x = 1,

LHS

a(1)² + b(1) + c

a + b + c

0

( It is given that a + b + c = 0 )

RHS

0

LHS = RHS

Hence, we can say that x = 1 is one root of the given equation as it satisfies the given equation.

Product of roots = c/a,

(1st root) × (2nd root) = c/a

x = 1 is a root of the given equation. Hence, substituting its value.

1 × (2nd root) = c/a

2nd root = c/a

So, x = c/a is also a root of the given equation.

Answer :-

So, roots of the equation are :

• 1 and

• c/a

Note :

As a + b + c = 0

c = -(b + a)

a = -(b + c)

So, we can write c/a as :

c/a = -(b + a)/a = -c/(b + c) = (b + a)/(b + c)