Question

x² - 2 (5+2k)x + 3(7+10k)=0​

Answer 1

Step-by-step explanation:

2(5+2k)k+3(7+10k)=0

⇒ Here, a=1,b=−2(5+2k),c=3(7+10k)

⇒ It is given that roots are real and equal.

∴ b

2

−4ac=0

⇒ [−2(5+2k)]

2

−4(1)[3(7+10k)]=0

⇒ 4(25+20k+4k

2

)−4(21+30k)=0

⇒ 100+80k+16k

2

−84−120k=0

⇒ 16k

2

−40k+16=0

⇒ 2k

2

−5k+2=0

⇒ 2k

2

−4k−k+2=0

⇒ 2k(k−2)−1(k−2)=0

⇒ (k−2)(2k−1)=0

⇒ k−2=0 and 2k−1=0

∴ k=2 and k=

2

1

Answer 2

Step-by-step explanation:

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