Question

Find the value of P for which 3x2 – 5x + p = 0 has equal roots.​

Answer 1

Answer:

Step-by-step explanation:

b²=4ac

25=4*3*p

p=25/12

Answer 2

Step-by-step explanation:

We have an quadratic equation,

$\sf 3x^2-5x+p = 0$

Comparing it with $\sf ax^2+bx+c$,

$\sf \boxed{\sf a= 3} \qquad \boxed{\sf b=-5} \qquad \boxed{\sf c=p}$

We know that, for a quadratic equation having two equal roots,

$\sf D=0 \implies b^2-4ac=0$

Puting the values of a,b and c,

$\sf (-5)^2-4(3)(p)=0$

It can be written as,

$\sf 25-12p=0$

Adding 12p on both sides of this equation,

$\sf 25-12p+12p=12p$

Cancelling out 12p on left hand side,

$\sf 25 -\cancel{12p} +\cancel{12p} =12p$

Can be written as,

$\sf 12p=25$

Dividing by 12 on both sides of this equation,

$\sf \dfrac{12p}{12}=\dfrac{25}{12}$

Cancelling out 12 on left hand side of this equation,

$\sf \dfrac{\cancel{12}p}{\cancel{12}}=\dfrac{25}{12}$

So, we get the required value of p which is are required answer,

$\sf \: \: \: \: \boxed{ \: \: \sf p=\dfrac{25}{12} \: \: \: }$