Question

Prove that If sin A and cos A are roots of the equation px² + qx + m = 0, then the relation among p, q and m is
q²+m² = (p+m)²

Answer 1

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Answer 2

Answer:

We call P the polynomial

P(x)=px2+qx+r

We know that both sin(α) and cos(α) are roots of P.

So we can rewrite P as

P(x)=p(x−sinα)(x−cosα)

Notice that p is the same variable as in the first expression of P(x), as it is the only one that has impact on x2

If we expand :

P(x)=px2−p(sinα+cosα)x+psinαcosα

Now we notice we have expression for q and r as well :

q=−p(sinα+cosα)

r=psinαcosα

Then one can calculate p2 , q2 , pr , (p−r)2 and (p+r)2 to find that correct answer is A.