Q. 54.4( 37 Votes )

If - 5 is a root

Answer :

Let f(x) = 2x2 + px - 15

As - 5 is a root of f(x)

⇒ f(- 5) = 0

⇒2(- 5)2 + p(- 5) - 15 = 0

⇒2(25) - 5p - 15 = 0

⇒50 - 15 = 5p

⇒5p = 35

⇒p = 7 [eqn 1]

Put the value of p in the quadratic equation p(x2 + x) + k = 0,

⇒ 7(x2 + x) + k = 0

⇒7x2 + 7x + k = 0

Any quadratic equation will have real roots if

b2 - 4ac = 0 [ for any quadratic eqn ax2 + bx + c]
Here, a = 7 , b = 7 and c = k

⇒72 - 4(7)(k) = 0
⇒49 - 28k = 0


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