Question

Find a quadratic polynomials whose zeroes are (4+√6) and (4-√6)

Answer 1

Given:

• Two zeroes of a quadratic polynomial are given.
• The zeroes are 4+√6 and 4-√6.

To Find:

• The quadratic polynomial whose zeroes are (4+√6) and (4-√6).

Concept Used:

• We will use the formula to find out the quadratic polynomial when its zeroes are given.

Answer:

Given zeroes to us are (4+√6) and (4-√6).

First of all its clear that the roots are conjugate to each other .

Formula:

$\large{\boxed{\red{\sf{\hookrightarrow p(x)=k[x^{2}-(\alpha+\beta)x+\alpha\beta]}}}}$

where

• $\alpha$ and$\beta$ are roots of polynomial.
• k is a constant.

Using this ,

$\sf{\implies p(x)=k[x^{2}-(4+\sqrt{6}+4-\sqrt{6})x+(4+\sqrt{6})(4-\sqrt{6})]}$

$\sf{\implies p(x) = k[x^{2}-(8)x +\{(4)^{2}-(\sqrt{6})^{2}\}]}$

using

• (a+b)(a-b) = a²-b².

$\sf{\implies p(x) = k[x^{2}-8x + (16-6)]}$

${\underline{\boxed{\red{\sf{\leadsto p(x)=k[x^{2}-8x+10]}}}}}$

Hence the required polynomial is k[x²-8x+10].