Question

3/5 is one of the two roots of 5x

²+ 2x + k = 0. Find its other root by first finding

the value of k​

Answer 1

Answer:

Step-by-step explanation:

Question

$5x^{2} +2x+k=0\\Given.\alpha =3/5\\we know that,\\\alpha +\beta =\frac{-b}{a} \\\frac{3}{5}+\beta = \frac{-2}{5} \\\beta =\frac{-2}{5} -\frac{3}{5\\}\\\beta =-1\\\alpha *\beta =\frac{c}{a} \\\frac{3}{5}*-1=\frac{k}{5} \\so,\\k=-3\\\alpha =\frac{3}{5} ,\beta =-1$

Answer 2

Step-by-step explanation:

given, one root x=3/5

so, => (x-3/5)=0

since x-3/5(calculated) is a factor of 5x²+2x+k=0.

so, (5x²+2x+k)/(x-3/5) must be divided

=> x-3/5)5x²+2x+k(5x+5

5x²-3x

_-____+__

5x+k

5x-3

__-_+__

k+3=0(difinetly)

so, k = -3.

so, the required equation is 5x²+2x-3=0.

And, other factor of the equation is quotient of the equation that is 5x+5.

so, other root will be 5x+5=0

=> 5(x+1)=0

=> x = -1.

that is your solutuon

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