Question

Solve the quadratic equation 3x^2 – 5x – 7 = 0
Give your answers to 3 significant figures.

Answer 1

Answer:

2.57 or -0.907

Step-by-step explanation:

→ First state the quadratic formula

$\frac{-b+-\sqrt{b^{2}-4ac } }{2a}$

→ Identify the 'a', 'b' and 'c' variables

$ax^{2} +bx+c$

$3x^{2} -5x-7$

a = 3, b = -5 and c = -7

→ Substitute in the values into the quadratic formula

$\frac{5+\sqrt{5^{2}-4*3*-7 } }{2*3}=\frac{5+\sqrt{25+84 } }{6}=\frac{5+\sqrt{109 } }{6}=2.573384418$

→ Do the same for negative

$\frac{5-\sqrt{5^{2}-4*3*-7 } }{2*3}=\frac{5-\sqrt{25+84 } }{6}=\frac{5-\sqrt{109 } }{6}=-0.9067177515$

Answer 2

The two solutions of the quadratic equation are:

• x = -2.573
• x = 0.907.

How to solve a quadratic equation?

For a general quadratic equation:

a*x^2 + b*x + c = 0

The solutions are given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}$

In this case we have:

3x^2 + 5x - 7 = 0

Then:

• a = 3
• b = 5
• c = -7.

Replacing that in the formula we get:

$x = \frac{-5 \pm \sqrt{5^2 - 4*3*(-7)} }{2*3}\\\\x = \frac{-5 \pm 10.44 }{6}$

Then the two solutions are:

• x = (-5 + 10.44)/6 = 0.907
• x = (-5 - 10.44)/6 = -2.573

If you want to learn more about quadratic equations, you can read:

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