Question

If alfa and B are the zeroes of the polynomial p(x)=x²-6x+k,then find the
value of K such that alfa²+B=40​

Answer 1

Answer:

k = -2

Step-by-step explanation:

The given equation is:

x^{2}-6x+kx

2

−6x+k , comparing this equation with ax^{2}+bx+c=0ax

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

a

−b

=6 and αβ=\frac{c}{a}

a

c

=kk

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

2

+β

2

=40

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

2

+β

2

=(α+β)

2

−2αβ

⇒40=(6)^{2}-2k40=(6)

2

−2k

⇒40-36=-2k40−36=−2k

⇒k=-2k=−2