Question

Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:

`q(x) = sqrt(3)x^2 + 10x + 7sqrt(3)`

Answer 1

`q(x)=sqrt3x^2+10x+7sqrt3=sqrt3x^2+7x+3x+7sqrt3`

`=sqrt3x(x+sqrt3)+7(x+sqrt3)`

`=(sqrt3x+7)(x+sqrt3)`

Zeros of the polynomials are `-sqrt3, (-7)/sqrt3`

Sum of zeros `=(-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.