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Question
If ๐ผ and ๐ฝ be the zeroes of the polynomial `2x^2 - 7x + k` write the value of (๐ผ + ๐ฝ + ๐ผ๐ฝ).
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Solution
By using the relationship between the zeroes of the quadratic polynomial.
We have
Sum of zeroes = `(-("Coefficient of x"))/("Coefficient of "x^2)`
Product of zeroes =`("Constant term")/("Coefficient of "x^2)`
a = 2, b = −7, and c = k
∴ ∝+ β = `(-b)/c`
= `(-(-7))/2`
= `7/2`
∝β = `c/a`
= `k/2`
Now, ๐ผ + ๐ฝ + ๐ผ๐ฝ = `7/2 + k/2`
= `(7 + k)/2`
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