Question

if -5 is a root of a quadratic equation p(x2+x) + k= 0 has equal roots, find the value of k

Answer 1

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${x}^{2} + x + k = 0 \\ \\ {( - 5)}^{2} + ( - 5) + k = 0. \\ \\ 25 - 5 + k = 0. \\ \\ 20 + k = 0 \\ \\ k = - 20.$

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Answer 2

Answer:

• Given -5 is the root of the Quadratic equation p(x)= (x²+X)+k

P(X) = x²+X+k✓

• If we will put the value of X= -5 then p(X)= 0 because given then Quadratic equation has equal roots

=> D=0✓ (b²-4ac=0)

Now

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$b ^{2} - 4ac = 0....(for \: equal \: roots) \\ \\ we \: have \: a = 1 \: b=1 \: and \: c = k \\ \\ \: therefore \: \\ \\ = > 1 ^{2} - 4 \times 1 \times k = 0 \\ \\ = > 1 - 4k = 0 \\ \\ = > - 4k = - 1 \\ \\ = > 4k = 1 .....(both \: side \: negative \: sign \: get \: cancelled \: out )\: \: \: \\ \\ = > k = \frac{1}{4}$

• The value of k = ¼