Question

if -5 is the root of the quadratic equation 2x power square +px -15 =0 and the quadratic equation p(x power square +x)+k=0 has equal roots, find the value of k???​

Answer 1

Given :-

• -5 is the root of the quadratic equation.

• Given quadratic equation :-

2x^2 + px - 15

• Second quadratic equation

= P(x^2 + x)k = 0 which has equal roots.

Solution :-

The quadratic equation is

2x^2 + px - 15 = 0

The root of quadratic equation x = -15

Therefore,

2( -15 )^2 + p(-15) - 15 = 0

2 * 225 - 15p - 15 = 0

450 - 15p - 15 = 0

435 - 15p = 0

-15p = -435

p = -435/-15

p = 29

The quadratic equation p ( x^2 + x) + k = 0 has equal roots.

px^2 + px + k

compare the given equation with ax^2 + bx + c = 0

a = p = 29 , b = p = 29 , c = k

Therefore,

The discriminant use for quadratic equation having real and equal roots is b^2 - 4ac

Put the required values,

( 29)^2 - 4 * 29 * k = 0

841 - 116k = 0

-116k = -841

k = -841/-116

k = 7.25 or 29/4

Hence, The value of K is 7.25 or 29/4 $.$

Answer 2

Answer:

K=29

4

Step-by-step explanation:

Hope it helps ✌️✌️