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If one root of the equation 2x2 + px - 5 = 0 is - 5 and the quadratic equation p(x^ - a) + k = 0
has equal roots, find the value of 'K.
Answers
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
Answer:
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
Step-by-step explanation: