Question

If alpha and beta are series of a x^2-8x+k such that alpha^2+beta^2=40. Find k

Answer 1

Answer:

Step-by-step explanation:

The given equation is:

x^{2}-6x+k, comparing this equation with ax^{2}+bx+c=0, we have a=1, b=-6, c=k.

Now, if α and β arethe two zeroes of the given polynomial, then α+β=\frac{-b}{a}=6 and αβ=\frac{c}{a}=k

Also, it is given that {\alpha}^{2}+{\beta}^{2}=40

⇒{\alpha}^{2}+{\beta}^{2}=({\alpha}+{\beta})^{2}-2{\alpha}{\beta}

⇒40=(6)^{2}-2k

⇒40-36=-2k

⇒k=-2

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