For the given quadratic expression f(x)=x2−2x+3. If M,m are the maximum and minimum values of the f(x) in [−1,2]. Then the value of M+4m is
A
−10
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B
10
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C
7
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D
−7
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Solution
The correct option is B10 Given: f(x)=x2−2x+3
On comparing with standard quadratic equation y=ax2+bx+c we get, a=1,b=−2,c=3.
Here a>0 which means the minimum value occure at x=−b2a. x=−(−2)2.1 ⇒x=1
f(1)=m=(1)2−2(1)+3=2
Now we will find the value of D D=b2−4ac=(−2)2−4.1.3 ⇒D=−8
D<0, this means the quadratic equation does not have any root, and the graph will look like this
Maximum value of f(x) occurs at either of the end points of the interval [−1,2]. ∴f(−1)=(−1)2−2(−1)+3=6
and f(2)=(2)2−2(2)+3=3