Alg3.2.9

Determine the values of p in the following quadratic equations if they have real roots i). $px^2+4x+1=0\,$

ii). $5px^2-8x+2=0\,$

i). Given $px^2+4x+1=0\,$

The condition that the roots be real is $b^2-4ac \ge 0\,$

Hence $(4)^2-4(p)(1)\ge 0,16-4p \ge 0,16=4p,p=4\,$

ii). Given $px^2+4x+1=0\,$

The condition that the roots be real is $b^2-4ac \ge 0\,$

Hence $(-8)^2-4(5p)(2)\ge 0,64-40p \ge 0,64=40p,p=\frac{8}{5}\,$