Question

if -5 is a root of the quadratic equation 2x^2+px-15=0 and roots of p(x² +x)+k=0 are equal roots,then find the value of p and k

Answer 1

2x² + px - 15 = 0

if -5 is root of the equation

⇒ When x = -5, the equation will return 0

Find p:

2(-5)²  + p (-5)  - 15 = 0

50 - 5p - 15 = 0

5p = 35

p = 7

p(x² + x) + k = 0

Since = 7:

7(x² + x) + k = 0

7x² + 7x + k = 0

The equation has equal roots

⇒ the discriminant = 0

Find k:

b² - 4ac = 0

7² - 4(7)(k) = 0

49 - 28k = 0

28k = 49

k = 49 ÷ 29

k = 1.75

Answer: p = 7 and k = 1.75

Answer 2

Given -5 as the root of eq.
finding the solution

2(-5)²+p(-5)-15=0

50-5p-15=0

5p=35
p=7


p(x²+x)+k=0

As,7

7(x²+x)+k=0

=7x²+7x+k=0

Then k,

b²-4ac=0
7²-4(7)(k)=0

49-28k=0

28k=49
k=1.75