Chapter 7: Q. 4 (page 464)

Find the real solutions of $x^{2} - x - 1 = 0$

Short Answer

Expert verified

The solution set is $\{\frac{1 + \sqrt{5}}{- 2}, \frac{1 - \sqrt{5}}{- 2}\}$ .

Step by step solution

Step 1. Given Information

We have to find the real solutions of $x^{2} - x - 1 = 0$

Step 2. The equation is in standard form, so we compare it to ax2+bx+c=0 to find a,b and c.

$x^{2} - x - 1 = 0 a x^{2} + b x + c = 0$

So $a = 1, b = - 1, c = - 1$

Step 3. With a=1, b=-1 and c=-1, we evaluate the discriminant b2-4ac.

$= b^{2} - 4 a c = {(- 1)}^{2} - 4 \times 1 \times (- 1) = 1 + 4 = 5$

Since $b^{2} - 4 a c \geq 0$ , there are two real solutions.

Step 4. We use the quadratic formula witha=1, b=-1, c=-1 and b2-4ac=5.

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} x = \frac{- (- 1) \pm \sqrt{5}}{2 \times (- 1)} x = \frac{1 \pm \sqrt{5}}{- 2}$

The solution set is $\{\frac{1 + \sqrt{5}}{- 2}, \frac{1 - \sqrt{5}}{- 2}\}$

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Find the real solutions of $x^{2} - x - 1 = 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The equation is in standard form, so we compare it to ax2+bx+c=0 to find a,b and c.

Step 3. With a=1, b=-1 and c=-1, we evaluate the discriminant b2-4ac.

Step 4. We use the quadratic formula witha=1, b=-1, c=-1 and b2-4ac=5.

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Find the real solutions ofx2-x-1=0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The equation is in standard form, so we compare it to ax2+bx+c=0 to find a,b and c.

Step 3. With a=1, b=-1 and c=-1, we evaluate the discriminant b2-4ac.

Step 4. We use the quadratic formula witha=1, b=-1, c=-1 and b2-4ac=5.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Mechanics Maths

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Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the real solutions of $x^{2} - x - 1 = 0$