Question

if-5 is a root of the quadratic equations 2x2+px-15=0 and the quadratic equation p(x2+x) +k=0 has equal roots. find the value of k.

Answer 1

As the -5 is root of this equation 2x²+px-15=0
so,x= -5
putting the value of x in quadratic equation
Now,2(-5)²+p×-5-15=0
2×25-5p-15=0
50-15=5p
35=5p
p=35/5=7
Again putting the value of p in another quadratic equation
px²+px+k=0
7x²+7x+k=0
a=7,b=7 and c=k
As the quadratic equation having the equal roots
so, D=0
and D=b²-4ac
b²-4ac=0
putting the values
7²-4×7×k=0
49-28k=0
49=28k
k=49/28
dividing by 7
k=7/4
I HOPE THIS WILL HELP YOU MARK ME BRAINLIEST

Answer 2

Given that one root is -5 

x = -5 

Putting the value of x in the equation,

2x² + px - 15 = 0 

2(-5)² + p(-5) = 15 

2(25) - 5p = 15 

50 - 5p = 15 

50 - 15 = 5p 

35 = 5p 

p = 35/5 

p =  7 
=====================

Now,


Given that p(x²+ x)+k = 0 has equal roots

putting the value of  p,


7(x² + x ) + k= 0 

7x² + 7x + k = 0

We know that, Discriminant = b²-4ac

(7)² - 4( 7 × k)

49 - 28k 

For equal roots, discriminant = 0 

49 - 28k = 0 


49 = 28 k 

49/28 = k 

7/4 = k




i hope this will help you


-by ABHAY