The value of p  for which both the roots of the equation 4x2−20px+(25p2+15p−66)=0  are less than 2, lies in the interval

The given equation is 4x2−20p x+(25p2+15p−66)=0      …..(1) As (1) has real roots, therefore,  (−20p)2  −4.4  (25p2+15p−66)≥0                (∵b2−4ac≥0) ⇒  −  240  p+1056  ≥  0  ⇒  p  ≤  225 Since, both the roots of the equation (1) are Less than 2, therefore, sum of the roots <4 ⇒    20p4<  4  ⇒  p<45 Now, if  f(x)  =4x2−20  px+25p2+15p  −66, Then graph of y=  f(x)   is an upward parabola meeting X− axis at points which lie on left of x=2 and hence f(2)>0 ⇒    16−40p+25p2+15p−66>0 ⇒      25p2−25p−50  >0 ⇒    p2−p−2>0  ⇒  (p−2)  (p+1)  >0 ⇒    p<−1    or  p>2 But p<  45,  therefore, p<−1 i.e. p∈(−∞,−1).