Question

If a+√b and a-√b are the zeroes of a polynomial, then find the polynomial.

Answer 1

Answer: Quadratic equation would be

x^2-2ax+a^2-b=0

Step-by-step explanation:

Since we have given that

First root = a+√b

Second root = a-√b

Sum of roots = a+√b+a-√b = 2a

Product of roots = (a+√b)(a-√b) =a^2-b

So, quadratic equation would be

x^2-2ax+a^2-b=0

Answer 2

Answer:

$x^2 - 2ax + (a^2 - b^2)$ is the quadriatic equation.

Step-by-step explanation:

Given:

If $a+ \sqrt b$and $a - \sqrt b$ are the zeroes of a polynomial, then find the polynomial.

Solution:

Let A and B be the rots of the polynomial,

A = $a+ \sqrt b$, B = $a - \sqrt b$

A + B – 2a,

A $\times$ B = $a^2 - b^2$

F(x) = $x^2 - 2ax + (a^2 - b^2)$

Result:

The quadriatic equation would be $x^2 - 2ax + (a^2 - b^2)$

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