Question

Find the zeros of the quadratic polynomial 9x² - 5 and verify the relation between the zeros and its coefficients.

Answer 1

We have,

`9x^2 - 5 = (3x)^2 - (sqrt5)^2 = (3x - sqrt5)(3x + sqrt5)`

So, the value of 9x² - 5 = 0

when `3x - sqrt5  = 0 `

i.e., when  x = `sqrt5/3` or x  = `(-sqrt5)/3`

Sum of the zeros

`= sqrt5/3 -  sqrt5/3 = 0 = -((0))/9 = -["coefficient of x"/("coefficient of"x^2)]`

Product of the zeros

`= (sqrt5/3)xx((-sqrt5)/3) = (-5)/9 =["coefficient of x"/("coefficient of"x^2)]`