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Mathematics : 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

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.

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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.

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45.

Is it possible to design a rectangular park of perimeter 80 m and area 400 m²? If so, find its length and breadth.

207 Views

Short Answer Type

46. State whether the following is quadratic equation:
(x – 2)² (x – 1) = (x – 4) (x + 3)

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47. State whether the following is quadratic equation:
(x – 4) (x – 3) = (x – 3) (x² – 4)

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48. State whether the following is quadratic equation:

square root of 2 straight x squared plus 4 straight x plus 5 square root of 2 plus 3 equals 0

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49. Write the nature of the roots of the following quadratic equation:

space space straight x squared minus 1 half straight x minus 4 equals 0.

611 Views

50. Write the nature of the roots of the following quadratic equation:

3 straight x squared minus 2 straight x plus 1 third equals 0

151 Views