Question

If -5is a root of 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

-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

Answer 2

Your answer is in attachment