Answer:
The equation [tex]5x^2\:+\:9x\:-\:2\:=\:0[/tex] has roots –2 and 1/5.
Hence, the option 'a' is the correct answer.
Step-by-step explanation:
Checking the equation
[tex]5x^2\:+\:9x\:-\:2\:=\:0[/tex]
putting x = -2 in the equation
[tex]5\left(-2\right)^2\:+\:9\left(-2\right)-\:2\:=\:0\:[/tex]
[tex]2^2\cdot \:\:5-9\cdot \:\:2-2=0[/tex]
[tex]2^2\cdot \:5-18-2=0[/tex]
[tex]20-20=0[/tex]
[tex]0=0[/tex]
L.H.S=R.H.S
putting x = 1/5 in the equation
[tex]5\left(\frac{1}{5}\right)^2\:+\:9\left(\frac{1}{5}\right)-\:2\:=\:0\:[/tex]
[tex]5\left(\frac{1}{5}\right)^2+9\cdot \:\frac{1}{5}-2=0[/tex]
[tex]\frac{1}{5}+\frac{9}{5}-2=0[/tex]
[tex]2-2=0[/tex]
[tex]0=0[/tex]
L.H.S=R.H.S
As putting x = -2 and x = 1/5 satisfy the equation.
Therefore, the equation [tex]5x^2\:+\:9x\:-\:2\:=\:0[/tex] has roots –2 and 1/5.
Hence, the option 'a' is the correct answer.
