Question

If a and B are the zeroes of the polynomial ax square+ bx + c, find the value of a² + B ²​

Answer 1

Step-by-step explanation:

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prajapatyk01

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Let given quadratic polynomial be,

f(x)=ax²+bx+c

Let A and B be the zeroes of f(x).

Then we know that,

A={-b+√(b²-4ac)}/2a

and,

B={-b-√(b²-4ac)}/2a

Now we have,

=A²

=[{-b+√(b²-4ac)}/2a]²

={b²-2b√(b²-4ac)+b²-4ac}/4a²

={2b²-4ac-2b√(b²-4ac)}/4a²

and

=B²

=[{-b-√(b²-4ac)}/2a]²

={b²+2b√(b²-4ac)+b²-4ac}/4a²

={2b²-4ac+2b√(b²-4ac)}/4a²

Now,

=A²-B²

={2b²-4ac-2b√(b²-4ac)}/4a²-{2b²-4ac+2b√(b²-4ac)}/4a²

={2b²-4ac-2b√(b²-4ac)-2b²+4ac-2b√(b²-4ac)}/4a²

={-4b√(b²-4ac)}/4a²

=-b√(b²-4ac)/a²

Hence,

A²-B²=-b√(b²-4ac)/a²

Answer 2

Step-by-step explanation:

If α and β are the roots of the polynomial ax2 + bx + c, then find the value of α2 + β2.