Question

If both the zeroes of a quadratic polynomial ax2 + bx + c are equal and opposite in sign, then ‘b’ is​

Answer 1

Answer:-

The Required Value of b is 0.

Explanation:-

Given:-

• A quadratic polynomial ax² + bx + c.

• The two zeroes of the polynomial are equal but opposite in sign.

To Find:-

• The value of b.

Concept Used:-

In a quadratic equation:- dx² + ex + f" if $\bf\alpha\:\:and\:\:\beta$ are its zeores then,

$\large\orange{ \longrightarrow \boxed{\red{ \bf \alpha + \beta = - \dfrac{e}{d}.}}}$

So Here,

• $\tt\alpha\:\:and\:\:\beta$ = $\gamma$ And $-\:\gamma$. (say).

• e = b.

• d = a.

Therefore,

By using concept,

$\tt\mapsto \gamma + ( - \: \gamma) = - \dfrac{b}{a} .$

$\tt\mapsto \gamma - \gamma = - \dfrac{b}{a} .$

$\tt\mapsto - \dfrac{b}{a} = 0.$

$\tt\mapsto - b = 0 \times a.$

$\tt\mapsto - b = 0.$

$\large\red{\mapsto \boxed{ \blue{ \bf b = 0.}}}$

Therefore the required value of b is 0.

Answer 2

Answer:

b is 0

Step-by-step explanation:

If both the zeroes of a quadratic polynomial ax² + bx + c are equal and opposite in sign.

Assume that the zero is "m".

As said in question, that the zero is same and equal and opposite in sign.

Zero = +m, -m

We have to find the value of b.

Sum of zeros = -b/a and Product of zeros = c/s

Sum of zeros = -B/A

Where A is a, B is b and C is c using quadratic polynomial.

→ +m -m = b/a

→ 0 = b/a

→ 0(a) = b

→ 0 = b

Hence, the value of b is 0.