Question

The equation mx2 + 12x + 9m = 0 has different roots for different values of m. For what values of m will the equation have one repeated root?

Answer 1

b^2 - 4ac = 0 
12^2 - 4m(9m) = 0 
144 = 36m^2 
m^2 = 4 
m = ± 2
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-TyyBenjii

Answer 2

Answer:

The value of m would be 2 or - 2.

Step-by-step explanation:

Since, a quadratic equation $ax^2+bx+c$ has two different real roots,

If $b^2-4ac> 0$

It has two equal real roots,

If $b^2-4ac=0$

While it has two different complex roots,

If $b^2-4ac<0$

Here, the given equation is,

$mx^2+12x+9m=0$

By comparing,

a = m, b = 12 and c = 9m,

By the above properties,

For equal roots,

$(12)^2-4(m)(9m)=0$

$144-36m^2=0$

$-36m^2 = -144$

$m^2 = 4\implies m\pm 2$

Hence, the value of m would be 2 or - 2.