# – Find a quadratic polynomials, whose zeroes are 4 – root 3 and 4 + V3.​

– Find a quadratic polynomials, whose zeroes are 4 – root 3 and 4 + V3.​

### 2 thoughts on “– Find a quadratic polynomials, whose zeroes are 4 – root 3 and 4 + V3.​”

The quadratic polynomial whose zeroes are

4 +√3 and 4 – √3

2. Step-by-step explanation:

If the Sum of zeroes and Product of the zeroes of a quadratic polynomial is given then the quadratic polynomial is

\sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }x

2

−(Sumofthezeroes)x+Productofthezeroes

EVALUATION

Here it is given that the zeroes of the quadratic polynomial are 4 +√3 and 4 – √3

Sum of the zeroes

\sf{ = (4 + \sqrt{3} ) + (4 – \sqrt{3} )}=(4+

3

)+(4−

3

)

= 8=8

Product of the Zeroes

\sf{ = (4 + \sqrt{3} ) (4 – \sqrt{3} )}=(4+

3

)(4−

3

)

\sf{ = {(4)}^{2} – {( \sqrt{3} )}^{2} }=(4)

2

−(

3

)

2

= 16 – 3=16−3

= 13=13

Hence the required Quadratic polynomial is

\sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }x

2

−(Sumofthezeroes)x+Productofthezeroes

\sf{ = {x}^{2} – 8x + 13}=x

2

−8x+13