Question

I will give brainlist​

Answer 1

Step-by-step explanation:

Given :-

ax^2+bx+c = 0

c≠0

α + β = -b/a

α β = c/a

To find :-

Find the value of (1/α^2) + (1/β^2) ?

Solution:-

Given quardratic equation is ax^2+bx+c = 0

Given that

Sum of the roots = -b/a

α + β = -b/a ------------(1)

Product of the roots = c/a

α β = c/a ------------(2)

Now , the value of (1/α^2) + (1/β^2)

=> (α^2+ β^2)/(α^2 β^2)

We know that a^2+b^2 = (a+b)^2 -2ab

=>[ (α + β)^2-2α β]/((α^2 β^2)

=> [ (α + β)^2-2α β]/((αβ)^2

=> [(-b/a)^2-2(c/a)]/(c/a)^2

=> [(b^2/a^2)-(2c/a)]/(c^2/a^2)

=> [(b^2-2ac)/a^2]/(c^2/a^2)

=> [(b^2-2ac)/a^2]× (a^2/c^2)

=> (b^2-2ac)/c^2

Answer:-

The value of (1/α^2) + (1/β^2) for the given problem is (b^2-2ac)/c^2

Option A

Used formulae:-

ax^2+bx+c = 0 is a quardratic equation then

• Sum of the roots = -b/a

• Product of the roots = c/a

• (a+b)^2-2ab = a^2+b^2