3x²-9x+x-3=0
find x or this quadratic equation
Answers
Answer:
Solution
=3
x=-1/3
Step-by-step explanation:
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Answer:
Class 11
>>Maths
>>Complex Numbers and Quadratic Equations
>>Quadratic Equations
>>Let f(x) = x^3 + 3x^2 + 9x ...
Question
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Let f(x)=x
3
+3x
2
+9x+6sinx then the roots of the equation
x−f(1)
1
+
x−f(2)
2
+
x−f(3)
3
=0 has
Medium
Solution
verified
Verified by Toppr
Correct option is
C
Two real roots
Given f(x)=x
3
+3x
2
+9x+6sinx
f(0)=0
f
′
(x)=3x
2
+6x+9+6cosx
=3(x+1)
2
+6(1+cosx)
f
′
(x)>0
∴f(x) is monotonically increasing graph
∴f(3)>f(2)>f(1)>f(0)
∴f(3)>f(2)>f(1)>0 (∵ if x
1
>x
2
⇒f(x
1
)>f(x
2
))
Let f(1)=a;f(2)=9;f(3)=c
g(x)=
x−f(1)
1
+
x−f(2)
2
+
x−f(3)
3
=0
(x−b)(x−c)+2(x−a)(x−c)+3(x−b)(x−a)=0
(x
=a,b,c)
3x
2
−(b+c+2a+2c+3b+3a)x+(bc+2ac+3ab)=0
3x
2
−(5a+4b+3c)x+(3ab+2ac+bc)=0
△=(5a+4b+3c)
2
−4(3)(3ab+bc+2ac)
=25a
2
+16b
2
+ac
2
+4ab+6ac+12bc
∴△>0(∵a>b>c>0)
∴g(x) has two distinct real roots.
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Step-by-step explanation:
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