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Question
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.
Solution
Given –5 is a root of the quadratic equation 2x2 + px – 15 = 0.
∴-5 satisfies the given equation.
∴ 2(5)2+ p(-5)-15 = 0
∴ 50 - 5p - 15= 0
∴ 35-5p = 0
∴5p = 35 ⇒ p = 7
Substituting p = 7 in p(x2 + x)+ k= 0,we get
7(x2+x)+k=0
∴7x2 + 7x + k = 0
The roots of the equation are equal.
∴ Discriminant b2 - 4ac = 0
Here, a=7, b=7, c=k
b2-4ac=0
∴ (7)2 - 4(7)(k)=0
∴ 49-28k= 0
∴28k = 49
∴ k = `49/28=7/4`
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