(3)
If the roots of the equation mx - 3mx + 9 = 0 are real and equal, find the
value of m.
Answers
Answer:
We know that while finding the root of a quadratic equation ax
2
+bx+c=0 by quadratic formula x=
2a
−b±
b
2
−4ac
,
if b
2
−4ac>0, then the roots are real and distinct
if b
2
−4ac=0, then the roots are real and equal and
if b
2
−4ac<0, then the roots are imaginary.
Here, the given quadratic equation x
2
−mx+9=0 is in the form ax
2
+bx+c=0 where a=1,b=−m and c=9.
(i) If the roots are equal then b
2
−4ac=0, therefore,
b
2
−4ac=0
⇒(−m)
2
−(4×1×9)=0
⇒m
2
−36=0
⇒m
2
=36
⇒m=±
36
⇒m=±6
(ii) If the roots are distinct then b
2
−4ac>0, therefore,
b
2
−4ac>0
⇒(−m)
2
−(4×1×9)>0
⇒m
2
−36>0
⇒m
2
>36
⇒m>±
36
⇒m>±6
(iii) If the roots are imaginary then b
2
−4ac<0, therefore,
b
2
−4ac<0
⇒(−m)
2
−(4×1×9)<0
⇒m
2
−36<0
⇒m
2
<36
⇒m<±
36
⇒m<±6
Hence m=±6 if the roots are equal, m>±6 if the roots are distinct and m<±6 if the roots are imaginary.
Step-by-step explanation:
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