Question

if one zero of polynomial 5 x square + PX + 10 is negative of order then find the value of p.​

Answer 1

$\large \dag$ Question :-

If one zero of polynomial 5x² + px + 10 is negative of other, then find the value of p.

$\large \dag$ Answer :-

$\large\underline{\pink{\underline{ \dashrightarrow\frak{\pmb{\text The \: \text Value \: of \: p \: is \: \text0 }}}}}$

$\large \dag$ Step by step Explanation :-

$\text{Let one zero of given polynomial} \\ \rm5x^2 + px + 10 \: \: be = \large\alpha$

According To Question As one zero of polynomial

5x² + px + 10 is negative of other,

$\large \rm\dashrightarrow \text{Second zero = } - \alpha$

We Know that, Sum zeros of any quadratic polynomial is :

$\bf \red\bigstar \: \: \orange{ \underbrace{ \underline{Sum = \frac{ - \: coefficiant \: of \: x}{ \: \: \: \: \: \: \: coefficiant \: of \: x {}^{2} } }}}$

We have the Given Polynomial as 5x² + px + 10 with zeros $\large\sf \alpha \: \: and \: - \alpha$

Therefore Using above written formula :

$:\longmapsto \rm Sum = \frac{ - p}{ \: \: 5}$

$:\longmapsto \rm \alpha + ( - \alpha ) = \frac{ - p}{ \: \: 5}$

$:\longmapsto \rm \alpha - \alpha = \frac{ - p}{ \: \: 5}$

$:\longmapsto \rm - p = 0$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf p = 0} }}}$

$\Large\underline{\pink{\underline{\frak{\pmb{\text Hence \: \text Value \: of \: p \: is \: \text 0 }}}}}$