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If \alpha, \beta are the zeroes of the polynomial f(x)=x^{2}-5 x+k such that \alpha-\beta=1, find the value of \mathrm{k}=?
CBSE | Class 10 | Excercise 2C | Maths | Polynomials | RS Aggarwal
If \alpha, \beta are the zeroes of the polynomial f(x)=x^{2}-5 x+k such that \alpha-\beta=1, find the value of \mathrm{k}=?

using the relationship between the zeroes of the quadratic polynomial.

Sum of zeroes =\frac{-(\text { coef ficient of } x)}{\text { coefficient of } x^{2}} and Product of zeroes =\frac{\text { constant term }}{\text { coef ficient of } x^{2}}

\therefore \alpha+\beta=\frac{-(-5)}{1} and \alpha \beta=\frac{k}{1}

\Rightarrow \alpha+\beta=5 and \alpha \beta=\frac{k}{1}

Solving \alpha-\beta=1 and \alpha+\beta=5, we will get

\alpha=3 and \beta=2

Substituting these values in \alpha \beta=\frac{k}{1}

k=6

i

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