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.
Quadratic Equations
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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.

KnowledgeBoat · Accepted Answer

As, -5 is the root of the quadratic equation 2x² + px - 15 = 0, so it will satisfy the equation. ∴ 2(-5)² + (-5)p - 15 = 0 ⇒ 2 × 25 - 5p - 15 = 0 ⇒ 50 - 5p - 15 = 0 ⇒ 5p = 35 ⇒ p = = 7. Substituting value of p in p(x² + x) + k = 0, we get : ⇒ 7(x² + x) + k = 0 ⇒ 7x² + 7x + k = 0 Since, above equation has real and equal roots. ∴ D = 0 ⇒ b² - 4ac = 0 ⇒ (7)² - 4 × 7 × k = 0 ⇒ 49 - 28k = 0 ⇒ 28k = 49 ⇒ k = . Hence, k = .

Mathematics

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.

Quadratic Equations

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