1
Question
The function f(x)=x3−7x2+25x+8 has exactly ______ roots.
The function f(x)=x3−7x2+25x+8 has exactly ______ roots.
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Solution
The correct option is B 1
Given : f(x)=x3−7x2+25x+8f′(x)=3x2−14x+25=03c2−14c+25=0b<0c=imaginaryHence there is no tangent to curveThus, the curve will intersect at x-axis only once as imaginary roots come in pair.Since there are only 3 roots of the given equation Two of them are imaginary and one is real.f(x)=0x3−7x2=−25x−8x2(x−7)=(−25−8)y1=x2(x−7)y2=−(25+8)The two curves intersects only ones between (−1,0)
Given : f(x)=x3−7x2+25x+8
f′(x)=3x2−14x+25=03c2−14c+25=0b<0c=imaginary
Hence there is no tangent to curve
Thus, the curve will intersect at x-axis only once as imaginary roots come in pair.
Since there are only 3 roots of the given equation
Two of them are imaginary and one is real.
f(x)=0x3−7x2=−25x−8x2(x−7)=(−25−8)y1=x2(x−7)y2=−(25+8)
The two curves intersects only ones between (−1,0)
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