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Re: If f(x^2) = x^4 6x^2 + 5, which of the following must be true? [#permalink]
KarishmaB can you provide a quick and easy solution to this question please ?

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Re: If f(x^2) = x^4 6x^2 + 5, which of the following must be true? [#permalink]
sayan640 wrote:
KarishmaB can you provide a quick and easy solution to this question please ?

Posted from my mobile device


The biquadratic function is symmetric in some line x^2=(5+1)/2=3
f(3+t)=f(3-t)

f(0)=f(6)=5.
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Re: If f(x^2) = x^4 6x^2 + 5, which of the following must be true? [#permalink]
Dint understand your solution.
Oppenheimer1945 wrote:
sayan640 wrote:
KarishmaB can you provide a quick and easy solution to this question please ?

Posted from my mobile device


The biquadratic function is symmetric in some line x^2=(5+1)/2=3
f(3+t)=f(3-t)

f(0)=f(6)=5.
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If f(x^2) = x^4 6x^2 + 5, which of the following must be true? [#permalink]
sayan640 wrote:
Dint understand your solution.
Oppenheimer1945 wrote:
sayan640 wrote:
KarishmaB can you provide a quick and easy solution to this question please ?

Posted from my mobile device

The biquadratic function is symmetric in some line x^2=(5+1)/2=3
f(3+t)=f(3-t)

f(0)=f(6)=5.


­Pls understand that the quadratic is symmertical. Let's say \(f(x)=x^2\), the function is symmetrical about y-axis or \(x=0.\) 
Hence we can say \(f(k)=f(-k)\),... the even function property.

here  \(x=0\) is the point of extrema. 

Same concept can be applied here after converting the bi-quadratic into a quadratic by basic substituon of \(x^2=t\).

the point of minima is the average of roots. Hence, function is symmertical about the line x= avg of root (1,5)=3.

Hence \( f(3+t)=f(3-t)­\)­ and option E follows
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If f(x^2) = x^4 6x^2 + 5, which of the following must be true? [#permalink]
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