If 2 is a root of the quadratic equation $3 x^{2} + a x - 2 = 0$ and the quadratic equation $a (x^{2} + 6 x) - b = 0$ has equal roots find the value of b.

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Solution

If 2 is root of the equation,
then substitute the value of x=2 in the equation,

The equation,
will be equal to,

For the equation to have equal roots, D=0
where D =

Then
900 - 4(5)(b)=0
900-20b=0
b=

So for the equation to have equal roots, b = 45

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If 2 is a root of the quadratic equation 3x2+ax−2=0 and the quadratic equation a(x2+6x)−b=0 has equal roots find the value of b.

If 2 is root of the equation, then substitute the value of x=2 in the equation, The equation, will be equal to, For the equation to have equal roots, D=0 where D = Then 900 - 4(5)(b)=0 900-20b=0 b= So for the equation to have equal roots, b = 45

If 2 is a root of the quadratic equation $3 x^{2} + a x - 2 = 0$ and the quadratic equation $a (x^{2} + 6 x) - b = 0$ has equal roots find the value of b.

If 2 is root of the equation,
then substitute the value of x=2 in the equation,

The equation,
will be equal to,

For the equation to have equal roots, D=0
where D =

Then
900 - 4(5)(b)=0
900-20b=0
b=

So for the equation to have equal roots, b = 45