Question

if the difference between the squares of each of the roots of (x^2 + px +45) is 216, then find the value of p?

Answer 1

A=alpha,b=beta

we can let ' a ' and ' b ' be the roots of the quadratic polynomial f (x) = x² + px + 45 
∴ we can  write a+b= -p (sum of the roots)
   we can also write ab=45(product of roots)
it is given that,
∴ (a + b)² –4ab=216
⇒ (– p)² –4×45=216
⇒ p ²–180=216
⇒ p²= 216+180
⇒p²=396
⇒p= ±√396
∴p=±19.89

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