Question

factorise the polynomial t^2-15

Answer 1

hello mate!.....

$given..... \\ \\ t {}^{2} - 15 \\ t {}^{2} - (\sqrt{15} ) {}^{2} \\ \\ we \: know... \\ (x {}^{2} - y {}^{2} ) = (x + y)( x - y) \\ then..... \\ (t + \sqrt{15} )(t - \sqrt{15} ) \\ \\ hope \: it \: helps \: u \: dear....$

Answer 2

The given polynomial is as follows :-

P(x) = t² - 15

We have two ways to factorise the polynomial.

☸️ By using identity:-

P(x) will be

$= {t}^{2} - {( \sqrt{15})}^{2} \\ \\ \\ = (t - \sqrt{15})(t + \sqrt{15})$

Equating with zeroes we get :-

$t = \pm \sqrt{15}$

☸️ Shridharacharya's Rule :-

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}$

Hence,

Since the coefficient of x is nothing in the given polynomial ; b=0

Hence,

$t = \frac{ \pm \sqrt{ - 4ac} }{2a} \\ \\ \\t = \frac{ \pm \sqrt{ - 4(1)( - 15)} }{2} \\ \\ \\t = \frac{ \pm2 \sqrt{15} }{2} \\ \\ \\t = \pm \sqrt{15}$