if alpha and beta are the zeroes of the quadratic polynomial fx =3x^2 -7x -6 ,find a polynomial whose zeroes are alpha square and beta square
Answers
Answer :
The given polynomial is f(x) = 3x² - 7x - 6
Since α and β are the zeroes of f(x),
α + β = - (- 7/3)
⇒ α + β = 7/3 .....(i)
αβ = - 6/3
⇒ αβ = - 2 .....(ii)
We need to find the polynomial whose roots are α² and β²
Now, α² + β²
= (α + β)² - 2αβ
= (7/3)² - 2 (- 2)
= 49/9 + 4
= (49 + 36)/9
= 85/9
⇒ α² + β² = 85/9
α²β² = (- 2)²
⇒ α²β² = 4
The polynomial having zeroes α² and β² be
g(x) = (x - α²) (x - β²)
= x² - (α² + β²) x + α²β²
= x² - (85/9) x + 4
= (9x² - 85x + 36)/9
Hence, the required polynomial be
g(x) = 9x² - 85x + 36
#MarkAsBrainliest
Answer:
9x^2 - 85x + 36
Step-by-step explanation:
fx = 3x^2 - 7x -6
to find zeroes
3x^2 - 9x +2x - 6 = 0
3x(x -3)+2(x-3) = 0
(3x+2)(x-3)= 0
x = -2/3 & 3
alpha = -2/3
Beta = 3
alpha^2 = 4/9
beta^2 = 9
(x-alpha^2)(x-Beta^2) = 0
(x-4/9)(x-9) = 0
(9x-4)(x-9) = 0
9x^2 - 85x + 36 = 0
so polynomial = 9x^2 - 85x + 36