Find the roots of 4x^2 - 5x = 3? In simplest radical form.

Question

Find the roots of 4x^2 - 5x = 3? In simplest radical form.

2 Answers

Impact of this question

2569 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-26T20:00:07

Use the formula $x_{1}, 2 = \frac{- b (+ or -) {(b^{2} - 4 \cdot a \cdot c)}^{\frac{1}{2}}}{2 \cdot a}$ $x_1,2=(-b(+or-)(b^2-4*a*c)^(1/2))/(2*a)$

Explanation:

Write the equation in form: $a x^{2} + b x + c = 0$ $ax^2+bx+c=0$
$4 x^{2} - 5 x - 3 = 0$ $4x^2-5x-3=0$
Apply the formula:
$x_{1} = \frac{5 + {(5^{2} - 4 \cdot 4 \cdot (- 3))}^{\frac{1}{2}}}{2 \cdot 4} = \frac{5 + {(25 + 16 \cdot 3)}^{\frac{1}{2}}}{8} = \frac{5 + {(25 + 16 \cdot 3)}^{\frac{1}{2}}}{2 \cdot 4} = \frac{5 + {(73)}^{\frac{1}{2}}}{8}$ $x_1=(5+(5^2-4*4*(-3))^(1/2))/(2*4)=(5+(25+16*3)^(1/2))/(8)= (5+(25+16*3)^(1/2))/(2*4)=(5+(73)^(1/2))/(8)$
$x_{2} = \frac{5 - {(5^{2} - 4 \cdot 4 \cdot (- 3))}^{\frac{1}{2}}}{2 \cdot 4} = \frac{5 - {(25 + 16 \cdot 3)}^{\frac{1}{2}}}{8} = \frac{5 + {(25 + 16 \cdot 3)}^{\frac{1}{2}}}{2 \cdot 4} = \frac{5 - {(73)}^{\frac{1}{2}}}{8}$ $x_2=(5-(5^2-4*4*(-3))^(1/2))/(2*4)=(5-(25+16*3)^(1/2))/(8)= (5+(25+16*3)^(1/2))/(2*4)=(5-(73)^(1/2))/(8)$
$4 x^{2} - 5 x - 3 = (x - \frac{5 + {(73)}^{\frac{1}{2}}}{8}) (x - \frac{5 - {(73)}^{\frac{1}{2}}}{8})$ $4x^2-5x-3=(x-(5+(73)^(1/2))/(8))(x-(5-(73)^(1/2))/(8))$

Answer 2 · 2018-03-26T20:11:00

$x = \frac{5}{8} \pm \frac{1}{8} \sqrt{73}$ $x=5/8+-1/8sqrt73$

Explanation:

$first rearrange the equation into standard form$ $"first rearrange the equation into standard form"$

$\Rightarrow 4 x^{2} - 5 x - 3 = 0 \leftarrow in standard form$ $rArr4x^2-5x-3=0larrcolor(blue)"in standard form"$

$solve for x using the quadratic formula$ $"solve for x using the "color(blue)"quadratic formula"$

$∙ x x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} \leftarrow quadratic formula$ $•color(white)(x)x=(-b+-sqrt(b^2-4ac))/(2a)larrcolor(blue)"quadratic formula"$

$here a = 4, b = - 5 and c = - 3$ $"here "a=4, b=-5" and "c=-3$

$x = \frac{5 \pm \sqrt{25 + 48}}{8}$ $x=(5+-sqrt(25+48))/8$

$x = \frac{5 \pm \sqrt{73}}{8}$ $color(white)(x)=(5+-sqrt73)/8$

$\Rightarrow x = \frac{5}{8} \pm \frac{1}{8} \sqrt{73}$ $rArrx=5/8+-1/8sqrt73$

Science

Math

Humanities

... and beyond

Find the roots of 4x^2 - 5x = 3? In simplest radical form.

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question