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If p and q are the roots of the equation x^2 = 7x + 4 , then show that      p^3 = 53p + 28 .

Asked by sudhanshubhushanroy 13th March 2018, 9:23 PM
Answered by Expert
Answer:
begin mathsize 16px style straight p space is space the space root space of space the space equation
rightwards double arrow straight p squared equals 7 straight p plus 4
rightwards double arrow straight p squared minus 7 straight p minus 4 equals 0
rightwards double arrow open parentheses straight p plus 7 close parentheses open parentheses straight p squared minus 7 straight p minus 4 close parentheses equals 0
rightwards double arrow straight p cubed minus 7 straight p squared minus 4 straight p plus 7 straight p squared minus 49 straight p minus 28 equals 0
rightwards double arrow straight p cubed minus 53 straight p minus 28 equals 0
rightwards double arrow straight p cubed equals 53 straight p plus 28 end style
Answered by Expert 14th March 2018, 9:10 AM
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