if one zero of cubic polynomial x^3-ax^2+x+3 is a then find value of a

1.	if one zero of cubic polynomial x^3-ax^2+x+3 is a then find value of a
Answer» Let p(x) = x3 + ax2 + bx + cAs -1 is one of the zeroes of p(x), p(-1) = 0⇒ (-1)3 + a(-1)2 + b(-1) + c = 0⇒\xa0- 1 + a – b + c = 0⇒ c = b –a + 1 …. (i)Let {tex}\\alpha{/tex}, β be two other zeroes of p(x),then product of zeroes =-1×\xa0{tex}\\alpha{/tex} × β ={tex}\\;\\;-\\frac{\\;\\;Cons\\tan t\\;term\\;}{coefficient\\;of\\;x^3}{/tex}⇒ (-1) (α β) = {tex}\\;\\;-\\frac{\\;\\;c}1{/tex}⇒ -\xa0{tex}\\alpha{/tex} β\xa0=\xa0- c⇒\xa0{tex}\\alpha{/tex} β\xa0= c⇒\xa0{tex}\\alpha{/tex} β = b –a + 1 [using (i)]\xa0Hence, the product of other two zeroes of the given cubic polynomial is b – a + 1.

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