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Question
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`q(x)=sqrt3x^2+10x+7sqrt3`
Solution
`q(x)=sqrt3x^2+10x+7sqrt3=sqrt3x^2+7x+3x+7sqrt3`
`=sqrt3x(x+sqrt3)+7(x+sqrt3)`
`=(sqrt3x+7)(x+sqrt3)`
Zeroes of the polynomials are `-sqrt3, (-7)/sqrt3`
Sum of zeroes `=(-10)/sqrt3`
`rArr-sqrt3-7/sqrt3=(-10)/sqrt3`
`rArr(-10)/sqrt3=(-10)/sqrt3`
Product of zeroes `=(7sqrt3)/3rArr(sqrt3x-7)/sqrt30=7`
`rArr7=7`
Hence, relationship verified.
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