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NDA 2022 Maths · Mathematics · Quadratic Equations · medium

The sum of all values of k for which x^2-2(k+1)x+(k+7)=0 has equal roots is

Single correct option

The sum of all values of kk for which x2−2(k+1)x+(k+7)=0x^2-2(k+1)x+(k+7)=0 has equal roots is
  1. A. 11
  2. B. −1-1
  3. C. −6-6
  4. D. 55
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Answer: (B) −1-1

Equal roots need discriminant 00: 4(k+1)2−4(k+7)=0⇒k2+k−6=04(k+1)^2-4(k+7)=0\Rightarrow k^2+k-6=0, i.e. k=2k=2 or k=−3k=-3. Their sum is −1-1 (also −ba-\frac{b}{a} of this quadratic). The product is −6-6, a distractor.
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