Question

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


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Answer 1

Here is your answer dear:-

In equation (2) I have added K by giving apostrophe.

I hope it will help you.
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Answer 2

Given Quadratic equation is 2x^2 + px - 15 = 0.

(i)

Given that -5 is a root of quadratic equation.

Substitute x = -5, we get

⇒ 2(-5)^2 + p(-5) - 15 = 0

⇒ 50 - 5p - 15 = 0

⇒ 35 - 5p = 0

⇒ p = 7.

(ii)

Given that p(x^2 + x) + k = 0 has equal roots.

Substitute p = 7, then the equation becomes:

⇒ 7(x^2 + x) + k = 0

⇒ 7x^2 + 7x + k = 0

Here, a = 7, b = 7, c = k.

∴ D = 0

⇒ b^2 - 4ac = 0

⇒ (7)^2 - 4(7)(k) = 0

⇒ 49 - 28k = 0

⇒ 49 = 28k

⇒ k = (7/4).

Therefore, the value of k = 7/4.

Hope this helps!