Q19 of 82 Page 4

If -5 is a root of the quadratic equation and the quadratic equation has equal roots, find the value of k. (CBSE 2014,2016)

For a quadratic equation, ax2 + bx + c = 0,


D = b2 – 4ac


If D = 0, roots are equal


Given, -5 is a root of the quadratic equation


⇒ 2 × 25 – 5p – 15 = 0


⇒ 35 = 5p


⇒ p = 7


Now, the quadratic equation has equal roots


⇒ 7x2 + 7x + k = 0 has equal roots


⇒ D = 49 – 28k = 0


⇒ k = 49/28 = 7/4

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