Question

Find a polynomial whose zeroes are tan2 45° and sec 60°.

Answer 1

$\Huge{\red{\underline{\textsf{Answer}}}}$

$x^{2} - 3x + 2$

Step-by-step explanation:

$\large{\red{\underline{\tt{Given:}}}}$

Let us assume that the zeroes of the polynomial = α and β

$\implies\rm α=tan 45°$

$\implies\rm β=sec 60°$

$\large{\red{\underline{\tt{To\:find:}}}}$

The polynomial=?

$\large{\red{\underline{\tt{Solution:}}}}$

$\implies\rm α=tan 45$........(given)

$\implies\rm α=1 (tan 45=1)$

$\implies\rm β=sec 60$.........(given)

$\implies\rm β=2$

Therefore, α=1 and β=2

The quadratic polynomial will be –

$\implies\rm x^2-(α+β)x+α.β$

$\implies\rm x^2-(1+2)x+1.2$

$\implies\rm x^2-3x+2$