Math, asked by vinuthkumar, 1 year ago

factorise the polynomial t^2-15

Answers

Answered by sg2544
14
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....

vinuthkumar: thank u sister
sg2544: welcome
Answered by skh2
3

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}

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