Question

If -1is a zero pf the polynomial p(x)=ax3+x²+x+4,find the value of a

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{-1\;is\;a\;zero\;of\;P(x)=ax^3+x^2+x+4}$

$\underline{\textbf{To find:}}$

$\textsf{The value of 'a'}$

$\underline{\textbf{Solution:}}$

$\textsf{Since -1 is a zero of P(x), P(-1)=0}$

$\implies\mathsf{a(-1)^3+(-1)^2+(-1)+4=0}$

$\implies\mathsf{a(-1)+1-1+4=0}$

$\implies\mathsf{-a+4=0}$

$\implies\mathsf{-a=-4}$

$\implies\boxed{\mathsf{a=4}}$

$\underline{\textbf{Find more:}}$

If the zeroes of cubic polynomial x3-15x2+74x-120 are the form a,a+b and a+2b for some positive real number, than the value of a and b are​

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Answer 2

x = -1 in p(x) = ax³ + x² + x + 4 = 0

a(-1)³ + (-1)² + (-1) + 4 = 0

-a + 1 - 1 + 4 = 0

-a = -4

so , a = 4