Chapter 11: Q. 306 (page 1069)

Solve the exercise
$16 y^{2} + 12 = - 32 x$

Short Answer

Expert verified

There is no solution to the equation.

Step by step solution

Step 1. Given information

The given equation $16 y^{2} + 12 = - 32 x$

Step 2. Simplify the quadratic equation

Simplifying the equation $(a - b) (a + b) = 0 a - b = 0 o r a + b = 0 a = b a = b o r a = - b Simplify the quadratic expression : 164 y^{2} + 12 = - 32 y [Given the expression] 16 y^{2} + 32 y + 12 = 0 [Write the quadratic equation of standard form] 4 (4 y^{2} + 8 y + 3) = 0 [Factor out 4 from expression] 4 (4 y^{2} + 6 y + 2 y + 3) = 0 [Since 8 y = 6 y + 2 y] 4 (2 y (2 y + 3) + 1 (2 y + 3)) = 0 [Factor out the common factor from group] 4 (2 y + 1) (2 y + 3) = 0 [Factor the common factor from expression] 4 ≃ 0 or 2 y + 1 = 0 or 2 y + 3 = 0 [Use the zero product property] o r y = - \frac{1}{2} o r y = - \frac{3}{2}$

Step 3. Checking the equation

$Check Substitute the value y = - \frac{1}{2} In the original equation . 16 y^{2} + 12 = - 32 [Given equation] 16 (- \frac{1}{2})^{2} + 12 = - 32 \frac{- 1}{2} * [Put y = - 1 / 2] 4 + 16 = 16 20 = 16 False Substitute the value y = - \frac{3}{2} in the original equation . 16 (- \frac{3}{2})^{2} + 12 = - 32 \frac{- 3}{2} [Put y = - 3 / 2] 48 + 12 = 48 60 = 16 False Hence there is no solution$

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Solve the exercise
$16 y^{2} + 12 = - 32 x$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the quadratic equation

Step 3. Checking the equation

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Solve the exercise16y2+12=-32x

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the quadratic equation

Step 3. Checking the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Mechanics Maths

Calculus

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Solve the exercise
$16 y^{2} + 12 = - 32 x$