Question

(b) Find the value of k. 2^12 ÷ 2^k/2 = 32​

Answer 1

Answer:

k=2 and k=1/2

Step-by-step explanation:

x²−2(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.

∴ b²−4ac=0

⇒ [−2(5+2k)] ²−4(1)[3(7+10k)]=0

⇒ 4(25+20k+4k²)−4(21+30k)=0

⇒ 100+80k+16k

2

−84−120k=0

⇒ 16k²−40k+16=0

⇒ 2k²−5k+2=0

⇒ 2k²−4k−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=1/2