Question

write the quadratic polynomal whose zeroes

are a+b and a – b
​

Answer 1

Answer:

a²-b²

Step-by-step explanation:

(a+b) (a-b)

= a²-b²

You can just multiple the two given zeroes to find the polynomial.

But the zeroes should not be Real numbers, that means in short they could be arbitrary constants or simply constants.

Answer 2

Step-by-step explanation:

Given -

• Zeroes are a+b and a-b

To Find -

• A quadratic polynomial

As we know that :-

• α + β = -b/a

→ (a+b) + (a-b) = -b/a

→ a + b + a - b = -b/a

→ 2a/1 = -b/a ..... (i)

And

• αβ = c/a

→ (a+b)(a-b) = c/a

→ a² - b²/1 = c/a ..... (ii)

Now,

From (i) and (ii), we get :-

a = 1

b = -2a

c = a²-b²

As we know that :-

For a quadratic polynomial :-

• ax² + bx + c

→ (1)x² + (-2a)x + (a²-b²)

→ x² - 2ax + (a²-b²)

Hence,

The quadratic polynomial is x² - 2ax + (a²-b²).