Question

If -5 is a root of the quadratic equation 2x^2+px-15=0 and the quadratic equation p(x^2+X)+k=0 has equal roots find k

Answer 1

HEY THERE!!

Question: If -5 is a root of the quadratic equation 2x^2+px-15=0 and the quadratic equation p(x²+X)+k=0 has equal roots find k

Method of Solution:

Find the Value of P in Quardratic Equation :

2x²+px-15 =0

Substitute the value of given roots in Equation;

f(x)=>  2x²+px-15 =0

=> 2(-5)² +p(-5) -15 =0

=> 2(25) -5p-15 =0

=> 50-5p-15 =0

=> 50-15 -5p =0

=> 35-5p =0

=> -5p =-35

•°• p = 7

Now, According to the Question;!

Quardratic Equation : p(x²+x)+k =0

Substitute the value of p in Equation;

f(p)=> p(x²+x)+ k =0

f(7) =>7(x²+x)+k =0

     => 7x²+7x+k =0

For Equal roots Discriminant must be 0

•°• 7x²+7x+k =0

°•° D = b²-4ac

=> (7)²-4.7.k = 0

=> 49 -28k =0

=> 49 = 28k

•°• k = 49/28

•°• k = 49/28

    K  = 7/4  

$\fbox{ \bold{Hence, Value \:  of  \: K \:  for  \: this \:   \: Equation   = \frac{7}{4} }}$