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Quadratic Equations

Short Answer Type

41. Find the values of k for each of the following quadratic equations, so that they have equal roots.
$space 2 straight x squared plus kx plus 3 equals 0$

We have,
$space 2 straight x squared plus kx plus 3 equals 0$
Here, $straight a equals 2 comma space straight b space equals straight k space and space straight c space equals space 3$
Now, $straight D equals straight b squared minus 4 ac space space space equals space left parenthesis straight k right parenthesis squared minus 4 left parenthesis 2 right parenthesis space left parenthesis 3 right parenthesis space space space equals space straight k squared minus 24$
For equal roots,
D = 0
$rightwards double arrow$ $straight b squared minus 4 ac equals 0$
$rightwards double arrow$ $space straight k squared minus 24 equals 0$
$rightwards double arrow$ $straight k squared equals 24$
$rightwards double arrow$ $straight k equals plus-or-minus square root of 24$
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106 Views

42. Find the values of k for each of the following quadratic equations, so that they have equal two roots.
kx (x – 2) + 6 = 0

115 Views

Long Answer Type

43. Is it possible to design a rectangular Mango grove whose length is twice its breadth and the area is 800 m²? If so, find its length and breadth.

162 Views

44.

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

201 Views