If α, β be the roots of ax2
+bx +c = 0, then value of α2
+ β2
is:
Answers
EXPLANATION.
α, β be the roots of the quadratic equation.
⇒ ax² + bx + c.
As we know that,
Sum of the zeroes of quadratic equation.
⇒ α + β = -b/a.
Products of the zeroes of quadratic equation.
⇒ αβ = c/a.
To find :
⇒ α² + β².
As we know that,
Formula of :
⇒ (x² + y²) = (x + y)² - 2xy.
Using this formula in the equation, we get.
⇒ α² + β² = (α + β)² - 2αβ.
Put the values in the equation, we get.
⇒ α² + β² = (-b/a)² - 2(c/a).
⇒ α² + β² = b²/a² - 2c/a.
⇒ α² + β² = b² - 2ac/a².
MORE INFORMATION.
Conjugates roots.
(1) = If D < 0.
One roots = α + iβ.
Other roots = α - iβ.
(2) = If D > 0.
One roots = α + √β.
Other roots = α - √β.
Given :-
If α and β are roots of ax² + bx + c
To Find :-
α² + β²
Solution :-
We know that
Sum = α + β = -b/a
Here
b = b
a = a
Sum = -(b)/a
Sum = -b/a
Product = αβ = c/a
Here
c = c
a = a
Product = c/a
Now
(α + β)² = (α²) + 2αβ + (β)²
(α + β)² = (α² + β²) + 2αβ
(α² + β²) = (α + β)² - 2αβ
α² + β² = (-b/a)² - 2(c/a)
α² + β² = (-b/a)² - 2 × c/a
α² + β² = (b²/a²) - 2c/a
α² + β² = b² - 2ac/a²