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

k = 1.75

Step-by-step explanation:

Given that x = - 5 is a root of the equation, then this value makes the equation true. Substitute x = - 5 into the equation and solve for p

2(- 5)² + p(- 5) - 15 = 0

50 - 5p - 15 = 0

- 5p + 35 = 0 ( subtract 35 from both sides )

- 5p = - 35 ( divide both sides by - 5 )

p = 7

Thus

7(x² + x ) + k = 0, that is

7x² + 7x + k = 0 ← in standard form

Using the discriminant Δ = b² - 4ac to find k

For equal roots then b² - 4ac = 0

with a = 7, b = 7 and c = k, then

7² - (4 × 7 × k) = 0

49 - 28k = 0 ( subtract 49 from both sides )

- 28k = - 49 ( divide both sides by - 28 )

k = 1.75

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