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if one of the zeroes of the cubic polynomial x^3+ax^2+bx+c is -1, then find the product of the other two zeroes

Posted by Jahnavi Arora 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 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)]

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CBSE > Class 10 > Mathematics