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 Reply
Answer:
The quadratic polynomial whose zeroes are
4 +√3 and 4 – √3
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