if  one zero of the polynomail (a2+4)x2+13x+4a is the reciprocal of the other,find the value of a.

Asked by manya.bhardwaj.01 | 22nd May, 2017, 12:08: PM

Expert Answer:

begin mathsize 16px style Let space one space zero space be space straight alpha.
Then comma space other space zero equals 1 over straight alpha
Given space quadratic space equation space is space left parenthesis straight a squared plus 4 right parenthesis straight x squared plus 13 straight x plus 4 straight a
Comparing space with space Ax squared plus Bx plus straight C comma space we space have
straight A equals straight a squared plus 4 comma space straight B equals 13 comma space straight C equals 4 straight a
Now comma space straight alpha cross times 1 over straight alpha equals fraction numerator 4 straight a over denominator straight a squared plus 4 end fraction
rightwards double arrow straight a squared plus 4 equals 4 straight a
rightwards double arrow straight a squared minus 4 straight a plus 4 equals 0
rightwards double arrow straight a squared minus 2 straight a minus 2 straight a plus 4 equals 0
rightwards double arrow straight a left parenthesis straight a minus 2 right parenthesis minus 2 left parenthesis straight a minus 2 right parenthesis equals 0
rightwards double arrow left parenthesis straight a minus 2 right parenthesis left parenthesis straight a minus 2 right parenthesis equals 0
rightwards double arrow left parenthesis straight a minus 2 right parenthesis squared equals 0
rightwards double arrow straight a minus 2 equals 0
rightwards double arrow straight a equals 2 end style

Answered by Rashmi Khot | 22nd May, 2017, 03:32: PM

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