Question

If the squared difference of the zeroes of the quadratic polynomial f (x) = x² + px + 45 is equal to 144 , 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=144
⇒ (– p)² –4×45=144  
⇒ p ²–180=144
⇒ p²= 144+180
⇒p²=324
⇒p= ±√324
∴p=±18