Question

Use the fact that the graph passes through (0,36) to find the coefficient a in f(x) = a(x + 3)(x + 1)(x - 2)(x – 3)

Answer 1

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

$\textsf{The graph of}\;\mathsf{f(x)=a(x+3)(x+1)(x-2)(x-3)}\;\textsf{passes through (0,36)}$

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

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

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

$\mathsf{Consider,}$

$\mathsf{f(x)=a(x+3)(x+1)(x-2)(x-3)}$

$\mathsf{Since\;the\;graph\;of\;f(x)=a(x+3)(x+1)(x-2)(x-3)}$

$\textsf{passes through (0,36), f(x) will be satisfied by (0,36)}$

$\implies\mathsf{f(0)=36}$

$\mathsf{a(0+3)(0+1)(0-2)(0-3)=36}$

$\mathsf{a(3)(1)(-2)(-3)=36}$

$\mathsf{a(18)=36}$

$\implies\mathsf{a=\dfrac{36}{18}}$

$\implies\boxed{\mathsf{a=2}}$

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

If 81x⁴-72x³+px²-8x+1 is a perfect square the find the value of p

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