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If one of the zeros of …

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If one of the zeros of the cubic polynomial x³+ax²+bx+c is -1 then find the product of the other two zeros
  • 1 answers

Sia ? 4 years, 9 months ago

Let p(x) = x3 + ax2 + bx + c
As -1 is one of the zeroes of p(x), p(-1) = 0
⇒ (-1)3 + a(-1)2 + b(-1) + c = 0
⇒ - 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× {tex}\alpha{/tex} × β ={tex}\;\;-\frac{\;\;Cons\tan t\;term\;}{coefficient\;of\;x^3}{/tex}
⇒ (-1) (α β)  =  {tex}\;\;-\frac{\;\;c}1{/tex}
⇒ - {tex}\alpha{/tex} β = - c
⇒ {tex}\alpha{/tex} β = c
⇒ {tex}\alpha{/tex} β = b –a + 1 [using  (i)]
 Hence, the product of other two zeroes of the given cubic polynomial is b – a + 1.

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