Question

Q. Find a cubic polynomial whose zeroes are 3, 1/2 and - 1

Answer 1

${ \bold{ \underline {\underline{\huge{\mathbb {\red{ ANSWER }}}}}}}$

$\mathrm{A \: cubic \: polynomial \: having \: α,} \\ \mathrm{ β, and \: γ as \: zeroesm is \: given by,}$

P(x) = x3 – (α + β + γ)x2 + (αβ + βγ + γα)x – (αβγ)

${\underline {\underline \mathtt \purple{Explanation}}}$

${\tt{\impliesα + β + γ = 0 + 1 + 2 = 3}} \\</p><p></p><p> \tt \impliesαβ + βγ + γα = 0 × 1 + 1 × 2 + 2 × 0 \\ </p><p> \tt \implies</p><p>αβ + βγ + γα = 0 + 2 + 0 = 2 \\ </p><p></p><p> \tt \impliesαβγ = 0 × 1 × 2 = 0</p><p></p><p>$

${\underline{\underline {\rm {\pink{Putting \: the \: values, we \: get},}}}}$

P(x) = x3 – (3)x2 + (2)x – (0)

P(x) = x3 – 3x2 + 2x

${ \orange { \boxed {\boxed{\therefore{(P) = {x}^{3} - {3x}^{2} + 2x}}}}}$