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Question

If the squared difference of the zeroes of the quadratic polynomial f(x)=x​​​​​​2+px+45 is equal to 144 find the value of p.


Solution

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)-(negative of coeff of x)
   we can also write ab=45(product of roots)-(constant)
it is given that,
(a - b)² =144
∴ (a + b)² –4ab=144 (calculate)
⇒ (– p)² –4×45=144  
⇒ p ²–180=144
⇒ p²= 144+180
⇒p²=324
⇒p= ±√324
∴p=±18


 

Mathematics

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