Chapter 9: Q.187 (page 906)

In the following exercises, solve equations in Quadratic Form for $x + 8 x^{\frac{1}{2}} + 7 = 0$ .

Short Answer

Expert verified

The equation has No solution for $x \in R$ .

Step by step solution

Step 1. Given Information.

The given equation is $x + 8 x^{\frac{1}{2}} + 7 = 0$ .

Step 2. Remove square roots

Simplify $x + 8 x^{\frac{1}{2}} + 7 = 0 x + 7 = - 8 x^{\frac{1}{2}}$

Squaring both sides , we get:-

${(x + 7)}^{2} = {(- 8 x^{\frac{1}{2}})}^{2} x^{2} + 14 x + 49 = 64 x x^{2} + 14 x - 64 x + 49 = 0 x^{2} - 50 x + 49 = 0$

Step 3. Solving quadratic equation .

Using Quadratic formula :-

$x^{2} - 50 x + 49 = 0$

$x_{1, 2} = \frac{- (- 50) \pm \sqrt{{(- 50)}^{2} - 4 \cdot 1 \cdot 49}}{2 \cdot 1} x_{1, 2} = \frac{- (- 50) \pm 48}{2 \cdot 1} x_{1} = \frac{- (- 50) + 48}{2 \cdot 1}, x_{2} = \frac{- (- 50) - 48}{2 \cdot 1} x = 49, x = 1$

Step 4. Verifying the solutions.

Substitute the value of $x = 49$ in $x + 8 x^{\frac{1}{2}} + 7 = 0$ , we get:-

$49 + 8 {(49)}^{\frac{1}{2}} + 7 = 49 + 8 \times 7 + 7 49 + 8 \times 7 + 7 = 112 112 \neq 0$

Similarly , Substitute $x = 1$ in the equation $x + 8 x^{\frac{1}{2}} + 7 = 0$ , we get:-

$1 + 8 {(1)}^{\frac{1}{2}} + 7 = 1 + 8 + 7 1 + 8 + 7 = 16 16 \neq 0$

Since, for $x = 49, x = 1$ the conditions are not satisfied. Therefore, There are No Solutions for the equation.

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In the following exercises, solve equations in Quadratic Form for $x + 8 x^{\frac{1}{2}} + 7 = 0$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Remove square roots

Step 3. Solving quadratic equation .

Step 4. Verifying the solutions.

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In the following exercises, solve equations in Quadratic Form for x + 8x12+ 7 = 0.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Remove square roots

Step 3. Solving quadratic equation .

Step 4. Verifying the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In the following exercises, solve equations in Quadratic Form for $x + 8 x^{\frac{1}{2}} + 7 = 0$ .