Question

A quadratic polynomial having zeroes `-sqrt(5/2)` and `sqrt(5/2)` is _________.

पर्याय

• `x^2 − 5sqrt2 x + 1`

• 8x² − 20

• 15x² − 6

• `x^2 - 2sqrt5 x - 1`

Answer 1

A quadratic polynomial having zeroes `-sqrt5/2` and `sqrt5/2` is 8x² − 20.

Explanation:

Let α and β be the zeroes of the quadratic polynomial.

Then, α = `-sqrt(5/2)` and `β = sqrt(5/2)`

Sum of Zeroes (α + β) = `-sqrt(5/2) + sqrt(5/2)` = 0

Product of zeroes (αβ) = `-sqrt(5/2) xx sqrt(5/2) = -sqrt((5 xx 5)/(2 xx 2)) = -5/2`

We know that a quadratic polynomial with zeroes α and β is given by

`x^2 - (α + β)x + αβ`

= `x^2 - (0)x + (-5/2)`

= `x^2 - (5/2)`

= `(2 x^2 - 5)/2`

= 2x² − 5

Multiply by 4, we get

= 8x² − 20