Question

one of the roots of equation 5m²+2m +k=0 is - 7/5. find the value of k

Answer 1

Here is the answer

Given Equation =>
$\bf{5m {}^{2} + 2m + k = 0}$

It's root is -7/5.

Solution

-7/5 is the root of the given quadratic Equation.

Substituting value of m in given Equation,

$\bf{5 (\frac{ - 7}{5} ) {}^{2} + 2 \times (\frac{ - 7}{5}) + k = 0}$

$\bf{\therefore \frac{49}{5} + (\frac{ - 14}{5} ) + k = 0}$

$\bf{ \frac{49}{5} - \frac{14}{5} + k = 0 }$

$\bf{\frac{35}{5} + k = 0}$

$\bf{7 + k = 0}$

$\bf{k = - 7}$

Value of k is -7.

Thanks!!

Answer 2

$\textbf{\huge{ANSWER:}}$

Equation:

${5m^2 + 2m + k}$

Given Root:

${(\frac{-7}{5}) }$

Put the value of m in the equation:

=》${5{(\frac{-7}{5})}^{2} + 2(\frac{-7}{5}) + k}$

=》$5 \times \frac{49}{25} - \frac{14}{5} + k = 0$

=》$\frac{49 - 14}{5} + k = 0$

=》$\frac{35}{5} = - k$

=》$( - 7) = k$