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प्रश्न
The sum and product of the zeros of a quadratic polynomial are \[- \frac{1}{2}\] and −3 respectively. What is the quadratic polynomial.
उत्तर
Let sum of quadratic polynomial is `a + ß = (-1)/2`
Product of the quadratic polynomial is `a ß = -3`
Let S and P denote the sum and product of the zeros of a polynomial as `(-1)/2 `and -3 .
Then
The required polynomial `g(x)` is given by
`g(x)=k (x^2-Sx +p)`
`=k[x^2-((-1)/2)x+(-3)]`
`= k [x^2+1/2x-3]`
Hence, the quadratic polynomial is `g(x)=k (x^2+x/2-3)`, where k is any non-zero real number
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