Question

If the product of the zeroes of the polynomial ax³-3x²+4x-6 is 6.
find the value of a.
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Answer 1

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p(x) = ax³ -3x² + 4x - 6

$\alpha \beta = \frac{c}{a} \\ \\ 6 = \frac{4}{a} \\ \\ a \: = \frac{2}{3}$

Answer 2

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$\huge \mathbb\fcolorbox{black}{lavenderblush}{Answer : ♡}$

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GIVEN :

➳ p(x) = ax³ - 3x² + 4x - 6

➳ Product of zeros : αβ = 6

PRODUCT OF ZEROS :

The product of zeros α and β is given as :

$\begin{gathered}\large {\boxed{\sf{\mid{\overline {\underline {\ ➳αβ= \: \frac{c}{a} ::}}}\mid}}}\\\\\end{gathered}$

p(x) = ax³ - 3x² + 4x - 6

General equation : ax³ + bx² + cx + d

Equating p(x) with general equations :

• a = a
• b = -3
• c = 4
• d = -6

Therefore, the Product of zeros c/a :

αβ = 6

c/a = 6

4/a = 6 (as αβ = c/a)

a = 4/6

$\boxed{a = 2/3}$

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$\begin{gathered}\large {\boxed{\sf{\mid{\overline {\underline {\star More\:To\:know\::}}}\mid}}}\\\\\end{gathered}$

$\begin{gathered}\qquad \qquad \boxed {\begin{array}{cc} \bf{\underline {\bigstar\:\: For \: a \:Quadratic \:Polynomial \::}}\\\\ \sf{ Whose \:\:zeroes \:\:are\:\:\alpha \:\&\;\: \beta\:\:} \\\\ 1)\:\: \alpha + \beta \: =\:\dfrac{-b}{a} \quad \bigg\lgroup \bf Sum\:of\;Zeroes \bigg\rgroup \\\\ 2)\:\: \alpha \times \beta \: =\:\dfrac{c}{a} \quad \bigg\lgroup \bf Product \:of\;Zeroes \bigg\rgroup \\\\ \end{array}} \end{gathered}$

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