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Irina-Kira [14]
3 years ago
15

Solve the quadratic equation 3x^2-5x-7=0

Mathematics
2 answers:
Murljashka [212]3 years ago
8 0

Step-by-step explanation:

3x^{2} -5x -7 = 0 \\ 3x^{2} -5x = 7 \\ x^{2} -\frac{5}{3}x = \frac{7}{3} \\ x^{2} -\frac{5}{3}x +\frac{25}{36} = \frac{7}{3} +\frac{25}{36} \\ (x -\frac{5}{6})^{2} = \frac{84 +25}{36} \\ (x -\frac{5}{6})^{2} = \frac{109}{36} \\ x -\frac{5}{6} = ±\sqrt{\frac{109}{36}} \\ x -\frac{5}{6} = ±\frac{\sqrt{109}}{6} \\ x = ±\frac{\sqrt{109}}{6} +\frac{5}{6}

Equation from the positive root:

x = \frac{\sqrt{109}}{6} +\frac{5}{6} \\ x = \frac{\sqrt{109} +5}{6}

Equation from the negative root:

x = -\frac{\sqrt{109}}{6} +\frac{5}{6} \\ x = \frac{-\sqrt{109} +5}{6}

<h3>Answer:</h3>

x = \frac{\sqrt{109} +5}{6}\\ and x = \frac{-\sqrt{109} +5}{6}\\ satisfy your quadratic equation.

Verdich [7]3 years ago
6 0

Given : A quadratic equation is given to us . The equation is 3x² - 5x - 7 = 0 .

To Find : The roots of the equation .

Solution : Given quadratic equation is 3x²-5x-7=0. So , let's factorise it to get the zeroes of the equation .

⇒ 3x² -5x - 7 = 0.

Here now , use Quadratic formula , of the quadratic equation in standard form of ax² + bx + c = 0.

\boxed{\red{\bf x\:\:=\:\:\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}}

On substituting respective values ,

⇒ x = -(-5) ± √ (-5)² - 4×3×(-7) / 2 × 3.

⇒x = 5 ± √ [ 25 + 84 ]/ 6 .

⇒ x = 5 ± √ 109 / 6 .

⇒ x = 5 + √109 / 6 , 5 - √109 / 6.

\purple{\underbrace{\underline{\boxed{\red{\tt \purple{\longmapsto} x = \dfrac{5+\sqrt{109}}{6}, \dfrac{5-\sqrt{109}}{6}}}}}}

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