Question

find the value of k for the following quadratic equations,so that they have two equal roots.

${x}^{2} - 2x(1 + 3k) + 7(3 + 2k) = 0$
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Answer 1

Answer:

k = 2, -10/9

Step-by-step explanation:

equation has equal roots

so

b^2= 4ac

{2(1+3k)}^2 = 4× 1× 7(3+2k)

{4(1+9k^2+6k)} = 28(3+2k)

(4 + 36k^2 +24k )= 84 + 56k

36k^2 - 32k -80=0

9k^2 - 8k - 20 = 0

9k^2 - (18-10)k-20=0

9k^2 - 18k +10k -20=0

9k(k-2) +10(k-2)=0

(k-2)(9k+10)=0

so when (k-2)=0

k= 2

and

(9k+10)=0

9k= -10

k= -10/9