kx(x-2)+ 6 = 0
kx2 - 2kx+6= 0
Since, roots of this equation are equal, then b2 = 4ac
(-2k)2 = 4 ×k ×6
K2 = 6k
=>k2-6k = 0
=>k(k - 6) = 0
k = 0 and 6
Case 1: For k=0, roots are undefined
Case 2: For k= 6, both roots are unity
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Select the option that is true regarding the following labelled Assertion (A) and Reason (R).
Assertion (A) | Reason (R) |
The system of equations: | System of equations |
On a particular day each of Danny, Edwin and Fahim sold three types of pens from their respective shops. Danny and Edwin sold an identical number of pens of Type A while Fahim sold twice as many pens of Type A as each of Danny and Edwin sold. The ratio of the numbers of pens of Type B sold by Danny, Edwin and Fahim was 3 : 5 : 2 respectively, while each of the trio sold an identical number of pens of Type C. The three sellers sold each of the types of pens at different prices per unit.
Assertion (A): It is possible that Danny sold each pen of Type A at a profit of Rs each pen of Type B at a loss of Re 1, and each pen of Type C at a loss of Rs 12 and made an overall profit of Rs 125; Edwin sold each pen of Type A at a profit of Rs 2, each pen of Type B at a loss of Rs 6, and each pen of Type C at a profit of Rs 6 and made an overall profit of Rs 110; and Fahim sold each pen of Type A at a profit of Re 1, each pen of Type B at a profit of Re 1, and each pen of Type C at a loss of Rs 3 and made an overall profit of Rs 210.
Reason (R): Framing and solving the three possible linear equations we will find that we get a unique solution.
Aman purchased 4 pens, 5 pencils and 8 scales for Rs. 120. Had Aman purchased 7 pens, 8 pencils and 11 scales, he would have to pay Rs. 192. Pankaj demanded 2 pens, 2 pencils and 2 scales. If Aman purchased only what was demanded by Pankaj, then how much would he have paid?
The sum of the reciprocals of the ages of two colleagues is nine times the difference of the reciprocals of their ages. If the ratio of the products of their ages to the sum of their ages is 100 : 9, Find their ages.