Question

recognize the quadratic equation in the following 13 p^2 =0.
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Answer 1

Step-by-step explanation:

We know that while finding the root of a quadratic equation ax2+bx+c=0 by quadratic formula x=2a−b±b2−4ac, 

if b2−4ac>0, then the roots are real and distinct 

if b2−4ac=0, then the roots are real and equal and

if b2−4ac<0, then the roots are imaginary.

Here, the given quadratic equation (3p+1)c2+2(p+1)c+p=0 is in the form ax2+bx+c=0 where a=(3p+1),b=2(p+1)=(2p+2) and c=p.

  

It is given that the roots are equal, therefore b2−4ac=0

⇒(2p+2)2−(4×(3p+1)×p)=0⇒(2p)2+22+(2×2p×2)−4(3p2+p)=0⇒(4p2+4+8p)−12p2−4p=0

Hence, p=−21 or p=1