Answered: "Using the quadratic formula, find the roots of:..."

Sheelmgal1p

Answered question

2021-11-21

Using the quadratic formula, find the roots of:

4 x^{2} + 7 x - 15 = 0

Answer can be left as fractions.

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

Answer & Explanation

Himin1945

Beginner2021-11-22Added 12 answers

Step 1
The quadratic formula is used when the roots of the quadratic equation cannot solved by the factorisation method.
Step 2
Here on comparsion of the quadratic equation

4 x^{2} + 7 x - 15 = 0

with the standard quadratic equation

a x^{2} + b x + c = 0

, it is observed that a is 4, b is 7 and c is -15. Therefore substitute these values in the equation

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

to find the value of x.

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

x = \frac{- 7 \pm \sqrt{7^{2} - 4 (4) (- 15)}}{2 (4)}

= \frac{- 7 \pm \sqrt{49 + 240}}{8}

= \frac{- 7 \pm \sqrt{289}}{8}

x = \frac{- 7 \pm 17}{8}

x = \frac{- 7 + 17}{8}

= \frac{5}{4}

x = \frac{- 7 - 17}{8}

= - 3

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