How do you use the discriminant to determine the nature of the solutions given $9m^2 + 24m + 16 = 0$ ?

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Answer 1 · 2017-02-05T14:46:46

$"roots are real and equal"$

$"For any quadratic equation "ax^2+bx+c=0" the nature of the roots depends on the discriminant "Delta=b^2-4ac$

$Delta>0 " roots are real and unequal"$

$Delta=0 " roots are real and equal"$

$Delta<0 " roots are complex"$

In this case:

$9m^2+24m+16=0$

$a=9, b=24, c=16$

$Delta=24^2-4xx9xx16$

$Delta=576-576=0$

$:. " roots are real and equal"$

this can be confirmed by factorising

$9m^2+24m+16=0=>(3m+4)^2=0$

How do you use the discriminant to determine the nature of the solutions given 9m^2 + 24m + 16 = 0 9m^2 + 24m + 16 = 0?