Question

Please answer the question [Q18] please do not answer only for points ... I had also searcher this question on google but unable to find answer please help me...​

Answer 1

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Question :

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

Solution :

The given quadratic equation is

  2x² + px - 15 = 0 .....(i)

Since (- 5) is a root of (i) no. equation, we can satisfy (i) no. equation with (- 5),

  2 (- 5)² + p (- 5) - 15 = 0

  ⇒ 2 (25) - 5p - 15 = 0

  ⇒ 50 - 5p - 15 = 0

  ⇒ 50 - 15 - 5p = 0

  ⇒ 35 - 5p = 0

  ⇒ 5p = 35

  ⇒ p = $\frac{35}{5}$

  ⇒ p = 7

Thus, the value of p is 7.

Another quadratic equation given is

  p (x² + x) + k = 0

  ⇒ 7 (x² + x) +k = 0

  ⇒ 7x² + 7x + k = 0

For equal roots, the value of the discriminant be 0

  D = 0

  ⇒ 7² - 4 ( 7 ) k = 0

  ⇒ (7 * 7) - (4 * 7) k = 0

  ⇒ 7 - 4k = 0

  ⇒ 4k = 7

  ⇒ k = $\frac{7}{4}$

Thus, the value of k is $\frac{7}{4}$ when the 2nd equation will be having equal roots.