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प्रश्न
Find the zeroes of the quadratic polynomial 2x2 – 11x + 15 and verify the relation between the zeroes and the coefficients.
Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:
2x2 – 11x + 15
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उत्तर
f(x) = 2x2 – 11x + 15
= 2x2 – (6x + 5x) + 15
= 2x2 – 6x – 5x + 15
= 2x(x – 3) – 5(x – 3)
= (2x – 5) (x – 3)
∴ f(x) = 0 ⇒ (2x – 5) (x – 3) = 0
⇒ 2x – 5 = 0 or x – 3 = 0
⇒ `x = 5/2` or x = 3
So, the zeroes of f(x) are `5/2` and 3.
Sum of zeroes = `5/2 + 3`
= `(5 + 6)/2`
= `11/2`
= `(-("Coefficient of x"))/(("Coefficient of" x^2))`
Product of zeroes = `5/2 xx 3`
= `(-15)/2`
= `("Constant term")/(("Coefficient of" x^2))`
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