If alpha and beta are the …
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Sia ? 6 years, 4 months ago
It is given that {tex} \alpha{/tex} and {tex} \beta{/tex} are the zeros of the polynomial {tex}f(x)=x^2-x-2{/tex}
Let,{tex}g(x)=k(x^2-Sx+P){/tex} be the required polynomial where 'S' is sum of zeroes and 'P' is product of zeroes.
Sum of zeroes of required polynomial (S)={tex}(2 \alpha+1)+(2 \beta+1)=2( \alpha+ \beta)+2=2 \times1+2=4{/tex}
Product of zeroes of required polynomial (P) = {tex}(2 \alpha+1) \times(2 \beta+1) = 4 \alpha \beta + 2 \alpha + 2 \beta + 1 = 4 \alpha \beta + 2 ( \alpha + \beta ) + 1{/tex}
{tex}=4 \times-2+2 \times1+1=-8+2+1=-5{/tex}
Hence, required polynomial g(x) is {tex}k(x^2-4x-5){/tex}, where k is any non-zero constant.
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