Question

Solve:

$4x + \frac{x - y}{8} = 17 \\ 2y + x - \frac{5y + 2}{3} = 2$
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Answer 1

Step-by-step explanation:

Given : one root of the equation 2x² + Px - 5 = 0 is - 5 and the quadratic equation p(x² + x) + k = 0 has equal roots.

To find : The value of k

solution : one root of the equation 2x² + px - 5 = 0 is -5

so, 2(-5)² + p(-5) - 5 = 0

⇒2 × 25 - 5p - 5 = 0

⇒45 - 5p = 0

⇒p = 9

now the quadratic equation p(x² + x) + k = 0

⇒9(x² + x) + k = 0

⇒9x² + 9x + k = 0

Discriminant = (9)² - 4(9)(k) = 0 [ for equal roots ]

⇒81 - 36k = 0

⇒k = 81/36 = 9/4

Therefore the value of k is 9/4