Question

if one root of the quadratic equation 5m^2 + 2m +k =0 is -7/5 then find the value of k by completing the following activity .
-7/5 the root of equation 5m^2 + 2m +k=0
-7/5 is satisfies the given equation
substituting m= -7/ 5 in given equation
5× ___ +2 × ___ +k =0
____+____+k= 0
7+k =0
k= _____​

Answer 1

Step-by-step explanation:

-7/5 the root of equation 5m^2 + 2m +k=0

hope it helps

Answer 2

Given that:- $5m^2 + 2m +k =0$

We have to find the value of '$k$'.

The root of the equation is $\frac{-7}{5}$,

By substituting the value of m = $\frac{-7}{5}$ in the given quadratic equation,

So, we will get

$=>5m^2 + 2m +k =0$

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

By simplifying it we get,

$=>5\times(\frac{49}{25} ) + 2\times(\frac{-7}{5} ) +k =0$

By cancelling the term, we get

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

Adding fractions that have a common denominator,

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

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

Reducing the fraction to its lowest term,

$=>7+k=0$

Subtract both sides by $7$

$=>k=-7$

Hence, the value of k is $-7.$

The root $\frac{-7}{5}$ satisfies the equation $5m^2 + 2m +k =0$.