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प्रश्न
Find the zeros of the polynomial f(x) = x2 + 7x + 12 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 + 7x + 12
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उत्तर
x2 + 7x + 12 = 0
⇒ x2 + 4x + 3x + 12 = 0
⇒ x(x + 4) + 3(x + 4) = 0
⇒ (x + 4) (x + 3) = 0
⇒ (x + 4) = 0 or (x + 3) = 0
⇒ x = – 4 or x = – 3
Sum of zeroes = – 4 + (– 3)
= `(-7)/1`
= `(-("Coefficient of " x))/(("Cofficient of " x^2))`
Product of zeroes = (– 4) (– 3)
= `12/1`
= `("Constant term")/(("Coefficient of " x^2))`
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