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प्रश्न
Find the zeroes of the quadratic polynomial f(x) = x2 + 3x – 10 and verify the relation between its zeroes and coefficients.
Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:
x2 + 3x – 10
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उत्तर
We have:
f(x) = x2 + 3x – 10
= x2 + 5x – 2x – 10
= x(x + 5) – 2(x + 5)
= (x – 2) (x + 5)
∴ f(x) = 0 ⇒ (x – 2) (x + 5) = 0
⇒ x – 2 = 0 or x + 5 = 0
⇒ x = 2 or x = –5.
So, the zeroes of f(x) are 2 and –5.
Sum of zeroes = 2 + (–5)
= –3
= `(-3)/1`
= `(-("Coefficient of" x))/(("Coefficent of" x^2))`
Product of zeroes = 2 × (–5)
= –10
= `(-10)/1`
= `("Constant term")/(("Coefficient of "x^2 ))`
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