Question

Show that 2 and - ⅓ are zeroes of the polynomial 3x² - 5x - 2​

Answer 1

✰ Qᴜēsᴛíõñ :-

Show that 2 and - ⅓ are zeroes of the polynomial 3x² - 5x - 2

✪ Söʟúᴛîøɴ :-

Given polynomial : p(x) = 3x³ - 5x - 2

p(2) = 3(2)² - 5(2) - 2

= 12 - 10 -2 = 12 - 12 = 0

p(-⅓) = 3(-⅓)² - 5(-⅓)-2

= ⅓ + 5/3 - 2

= 2 - 2 = 0

⛬ 2 and -⅓ are zeroes of p(x)

Answer 2

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Show that 2 and - ⅓ are zeroes of the polynomial 3x² - 5x - 2

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$3 {x}^{2} - 5x - 2 = 0 \\ = > 3 {x}^{2} - 6x + x - 2 = 0 \\ = > 3x(x - 2) + 1(x - 2) = 0 \\ = >( 3x + 1)(x + 2) = 0 \\ = > \green{ \boxed{x = 2} }\\ = > \green{\boxed{x = - \frac{1}{3} }}$

hope it helps you