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प्रश्न
Find the quadratic polynomial, sum, and product of whose zeroes are −1 and −20 respectively. Also, find the zeroes of the polynomial so obtained.
उत्तर
We have been given the sum of zeroes and product of zeroes
Let us consider the general polynomial
`p(x) = ax^2 + bx + c`
Sum of zeroes is `(-b)/a`
And product of zeroes is `c/a`
According to question
`(-b)/a = -1 "and" c/a = -20`
Assuming a = 1
-b = -1
⇒ b = 1
And c = -20
So, the polynomial so formed is `p(x) = x^2 + x - 20`
To find the zeroes of the polynomial equate polynomial to zero.
`x^2 + x - 20 = 0`
`x^2 + 5x - 4x - 20 = 0`
`x(x + 5) - 4(x + 5) = 0`
(x + 5)(x - 4) = 0
⇒ x = -5,4
Therefore, zeroes of the polynomial are -5 and 4.
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