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Question
The function f is defined by f(x)=2x3+3x2+cx+8, where c is a constant. In the xy-plane, the graph of f intersects the x-axis at the three points (−4,0),(12,0) and (p, 0). What is the value of c?
The function f is defined by f(x)=2x3+3x2+cx+8, where c is a constant. In the xy-plane, the graph of f intersects the x-axis at the three points (−4,0),(12,0) and (p, 0). What is the value of c?
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Solution
The correct option is B -18
- Given function f(x)=2x3+3x2+cx+8
- The roots are −4,1/2,p
- So product of roots is −2p=−8/2=−4 , which implies p=2
- Therefore c/2=2×1/2+2×(−4)+1/2×(−4)=−9
- Which implies c=−18
- Given function f(x)=2x3+3x2+cx+8
- The roots are −4,1/2,p
- So product of roots is −2p=−8/2=−4 , which implies p=2
- Therefore c/2=2×1/2+2×(−4)+1/2×(−4)=−9
- Which implies c=−18
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