Question

for what value of p quadratic equation px (x-4)+64=6 has equal roots p is not equal to 0​

Answer 1

px( x-4) + 64 -6= 0

px^2 -4px + 58= 0

For equal roots

discriminant = 0

16 p^2 -4p(58) = 0

16 p= 4(58)

p = 29/2

Answer 2

Given: Quadratic equation $px(x-4)+64=6$ has equal roots

To find: The value of p

Step-by-step explanation:

As we have

$px(x-4)+64=6 \\\\\Rightarrow px^2-4px+64-6=0\\\\\Rightarrow px^2-4px+58=0$

Now As the quadratic equation have equal roots then

$D= b^2-4ac$ where D is discriminant  and a, b, c are the coefficient of quadratic equation $ax^2+bx+c=0$

Therefore

a= p , b= -4p , c= 58

$D= (-4p)^2-4\times p\times 58\\\\\Rightarrow 0= 16p^2-4\times 58 \times p\\\\\Rightarrow 0= 8p(2p-29p)\\\\\Rigtarrow \text {Either } 8p = 0 \text { or } 2p-29 =0\\\\\text { But } p \neq 0 \therefore 2p-29 =0\\ \\p =\dfrac{29}{2}$

Hence the value of p is  $\dfrac{29}{2}$