Question

2. If a and B are the zeroes of the polynomial 2x^2 +7x + 3,then form a polynomial whose
zeroes are 1/a and 1/b

Answer 1

Answer:

$\huge{\boxed{\boxed{\sf{3x^{2}+7x+2}}}}$

Step-by-step explanation:

$\huge{\boxed{\boxed{\underline{\sf{SOLUTION-}}}}}$

$2 {x}^{2} + 7x + 3 = 0 \\ 2 {x}^{2} + 6x + x + 3 = 0 \\ 2x(x + 3) + 1(x + 3) = 0 \\( 2x + 1) (x + 3) = 0 \\ = )2x + 1 = 0 \\ = )2x = - 1 \\ = )x = \frac{ - 1}{2} - - - - - 1st \: zeroes \\ = ) x + 3 = 0 \\ = )x = - 3 - - - - - 2nd \: zeroes \\ \\ = )a = \frac{ - 1}{2} \\ = ) b = - 3 \\ \\ > > new \: zeroes \: of \: new \: quadratic \\ = )\frac{1}{a} = \frac{1}{ \frac{ - 1}{2} } = - 2 - - - - - 1st \: zeroes\\ = ) \frac{1}{b} = \frac{1}{ - 3} = \frac{ - 1}{3} - - - - - 2nd \: zeroes \\ \\ (x - \frac{1}{a} )(x - \frac{1}{b} ) = 0\\ = )(x - ( - 2))(x - ( \frac{ - 1}{3} )) = 0\\ = )(x + 2)(x + \frac{1}{3} ) = 0 \\ = )(x + 2)( \frac{3x + 1}{3} ) = 0 \\ = )(x + 2)(3x + 1) = 0 \\ = )3 {x}^{2} + 6x + x + 2 = 0 \\ = ) 3{x}^{2} + 7x + 2 = 0$

$\huge{\boxed{\boxed{\sf{3x^{2}+7x+2}}}}$

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