Question

if one zero of quadratic polynomial p(x)equal x2+2kx-25 is negative i
of the other find the value of k​

Answer 1

$\large{\underline{\boxed{\text{Given:}}}} </p><p>$

• One zero pf the polynomial is negative of the other
• p(x) = x² +2kx -25

$\large{\underline{\boxed{\text{To find:}}}} </p><p>$

• The value of k

$\large{\underline{\boxed{\text{Solution:}}}} </p><p>$

We have,

$\text{p(x) =} \text{ {x}}^{2} + \text{2kx - 25}$

Let the first zero be$\: \alpha\:$, then the other one will be$\: - \alpha$

$\underline{\text{Sum of zeroes}} = \alpha + ( - \alpha ) = 0$

We also know that,

$\underline {\text{Sum of zeroes}} = \frac{ -\text{ coefficient of x}}{\text{\: \: \:coefficient of {x}}^{2} }$

$\implies \text{ Sum of zeroes = } \frac{ - 2k}{ \: \: \: 1}$

This implies

$\alpha + ( - \alpha ) = \frac{ - 2k}{ \: \: \: 1} \\ \\ \implies \text{ - 2k = 0} \\ \\ \implies \textsf{k = } \frac{\: \: \: 0}{ - 2} \\ \\ \implies \boxed{\textsf{ \green{k = 0}}}$