Question

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

Answer 1

Answer:

7/4

Step-by-step explanation:

-5 is a root of quadratic equation 2x² + px - 15 = 0

so, 2(-5)² + p(-5) - 15 = 0

=> 50 - 5p - 15 = 0

=> 35 - 5p = 0

p = 7

now, put p = 7 in second quadratic equation,

p(x² + x ) + k = 0

=> 7(x² + x ) + k = 0

=> 7x² + 7x + k = 0

above equation has equal roots

so, D = b² - 4ac = 0

=> 7² - 4 × 7 × k = 0

=> 7 - 4k = 0

=> k = 7/4 = 1.75

hence, the value of k = 1.75