Q16) If beta and Alpha are the zeroes of the quadratic polynomial -
F(x) = x² - 6x +8, Find the value of a'+B7.
Answers
Answer:
f(x)=x
2
−3x+2
is the required polynomial.
Step-by-step explanation:
We are given the following polynomial:
x^2-6x+8x
2
−6x+8
To find the zeroes of the polynomial:
\begin{gathered}x^2-6x+8 = 0\\x^2-4x-2x+8 = 0\\x(x-4) - 2(x-4) = 0\\(x-4)(x-2) = 0\\x-4 = 0, x - 2 =0\\x = 4, x = 2\\\alpha = 4, \beta = 2\end{gathered}
x
2
−6x+8=0
x
2
−4x−2x+8=0
x(x−4)−2(x−4)=0
(x−4)(x−2)=0
x−4=0,x−2=0
x=4,x=2
α=4,β=2
New zeroes of polynomial:
\begin{gathered}\alpha' = \dfrac{\alpha}{2},\beta' = \dfrac{\beta}{2}\\\\\alpha' = 2, \beta' = 1\\\alpha' + \beta' = 3\\\alpha'\beta' = 2\end{gathered}
α
′
=
2
α
,β
′
=
2
β
α
′
=2,β
′
=1
α
′
+β
′
=3
α
′
β
′
=2
New polynomial:
\begin{gathered}x^2-(\alpha' + \beta')x + \alpha'\beta'\\f(x) = x^2 -3x +2\end{gathered}
x
2
−(α
′
+β
′
)x+α
′
β
′
f(x)=x
2
−3x+2
is the required polynomia