Question

Find the nature of the root of the equation
$9x { }^{2} - 6x + 4 = 0$
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Answer 1

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Since, 9x² +6kx+4=0 has equal roots.

Then, b²−4ac⩾0

(6k)²−4(9)(4)⩾0

36k ² −36(4)⩾0

36(k²−4)=0

k²−4=0

k² =2²

k=±2

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Let us check!!

9x²+6(2)x+4=0

9x² +12x+4=0

9x²+6x+6x+4=0

3x(3x+2)+2(3x+2)=0

(3x+2)(3x+2)=0

∴x= -2/3,-2/3

Answer 2

9 x

2

-6 x=0

3 x ( 3 x-२ )=0

x=0 ,

3

2