Question

Find the quadric Polynomial whose sum of zeros and product of zeros are root 2+1 and 1/2+1​

Answer 1

answer is 3x^2-3√2x+1 is the polynomial

Answer 2

Step-by-step explanation:

$Let, \: \alpha \: and \: \beta \: be \: the \: zeroes$

$\mathtt{Given :-}$

$\implies\alpha = 2 + 1 = 3$

$\implies \beta = \frac{1}{2} + 1 = \frac{3}{2}$

$\bull \: sum \: of \: zeroes \: = \alpha + \beta = 3 + \frac{3}{2} = \frac{9}{2}$

$\bull \: product \: of \: zeroes = \alpha \times \beta = 3 \times \frac{3}{2} = \frac{9}{2}$

$\mathfrak{We \: know \: that,}$

${x }^{2} - ( \alpha + \beta )x + ( \alpha \times \beta ) = 0$

${x}^{2} - ( \frac{9}{2} )x + \frac{9}{2} = 0$

${x}^{2} - ( \frac{9}{2} )x + \frac{9}{2} =0 \: \: is \: the \: required \: poynomial$