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Quadratic Equations

Short Answer Type

161. Find the roots of the quadratic equation by using quadratic formula:

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162. Find the roots of the quadratic equation by using quadratic formula:

9 straight x squared plus 12 straight x plus 4 equals 0

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163. Find the roots of the quadratic equation by using quadratic formula:
$straight x squared plus straight x minus 156 equals 0$

Solution not provided.
Ans. x = 12, -13

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164. Find the roots of the quadratic equation by using quadratic formula:

space space space space straight y squared equals 41 straight y minus 400.

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165. Use quadratic formula to solve the following equation for x:
abx² + (b² – ac) x – bc = 0.

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166. Use quadratic formula to solve the following equation for x:
9x² – 9 (a + b)x + (2a² + 5ab + 2b²) = 0.

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167. Use quadratic formula to solve the following equation for x:
a²x² + (a² – b²)x – b² = 0.

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168. A two digit number is such that the product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.

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Long Answer Type

169. Sum of the areas of two squares is 260 m². If the difference of their perimeters is 24 m, then find the sides of the two squares.

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Short Answer Type

170. The sum of the squares of two consecutive odd numbers is 394. Find the numbers.

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