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Question
If ๐ผ, ๐ฝ are the zeroes of the polynomial `f(x) = x^2 – 5x + k` such that ๐ผ - ๐ฝ = 1, find the value of k = ?
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Solution
By using the relationship between the zeroes of the quadratic polynomial.
We have
Sum of zeroes=`(-("Coefficent of x"))/("Cofficient of x"^2)` and Product of zeroes =`("Constant term")/("Coefficent of "x^2)`
`∴ ∝+β=-(-5)/1` and ∝β=k/1`
Solving ๐ผ - ๐ฝ = 1 and ๐ผ + ๐ฝ = 5, we will get
∝=3 and ๐ฝ=2
Substituting these values in ๐ผ๐ฝ =`k/1` we will get
`k = 6`
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