Evaluatethefollowing
If alpha and beta are the zeros of the polynomial f(x)5x
2+4x–9 then alpha^2+beta^2
Answers
Answer:
5x2 +4x-9
factorise the eq.
(5x +9)(x-1)=0
Then X = -9/5and beta=1
1.-4/5
2.106/25
3.54/25
Last three points you can solve.......
By the value of alphA and bEta
............this answer..............
Help you...........
...........Guys............
Step-by-step explanation:
Answer:
(Alpha)² + (Beta)² = 106/25
Step-by-step explanation:
This problem can be solved in two ways
1st method
5x² + 4x - 9 = 0
ax² + bx + c = 0
where a = 5, b = 4 and c = -9
Let the zeroes be A and B
We know that,
Sum of zeroes = -b/a
A + B = -4/5-----1
also,
Product of zeroes = c/a
A × B = -9/5
AB = -9/5-----2
so,
(A + B)² = A² + B² + 2AB
From eq.1 and eq.2 we know that
A + B = -4/5 and AB = -9/5
Thus,
Putting it in the identity, we get
(-4/5)² = A² + B² + 2(-9/5)
(16/25) = A² + B² + (-18/5)
Thus,
A² + B² = (16/25) - (-18/5)
A² + B² = (16/25) + (90/25)
A² + B² = ((90 + 16)/25)
A² + B² = 106/25
Hence,
(Alpha)² + (Beta)² = 106/25
2nd method
5x² + 4x - 9 = 0
ax² + bx + c = 0
where a = 5, b = 4 and c = -9
By splitting the middle term method we get
Sum = b = 4
Product = a × c = 5 × -9 = -45
Thus, factors are 9 and -5
so,
5x² + 4x - 9 = 0
5x² + 9x - 5x - 9 = 0
x(5x + 9) -1(5x + 9) = 0
(x - 1)(5x + 9) = 0
Thus,
x (alpha) = 1
OR
x (beta) = -9/5
(alpha)² + (beta)² = 1² + (-9/5)²
= 1 + (81/25) = (25/25) + (81/25)
= (81 + 25)/25 = 106/25
Therefore,
(alpha)² + (beta)² = 106/25
Hope you understood it........All the best