"Find the roots of the quadratic polynomials: 6x2+5x−1..." was answered by our community

Cheyanne Leigh

Answered question

2021-09-07

Find the roots of the quadratic polynomials:

6 x^{2} + 5 x - 1

4 x^{2} + 4 x - 4

Laaibah Pitt

Skilled2021-09-08Added 98 answers

Given:

6 x^{2} + 5 x - 1

The roots of

a x^{2} + b x + c

are

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

The roots of

6 x^{2} + 5 x - 1

x = \frac{- 5 \pm \sqrt{5^{2} - 4 (6) (- 1)}}{2 (6)}

x = \frac{- 5 \pm \sqrt{25 + 24}}{12}

x = \frac{- 5 \pm \sqrt{49}}{12}

x = \frac{- 5 \pm 7}{12}

x = - \frac{12}{12}, \frac{2}{12}

x = - 1, \frac{1}{6}

The roots of

6 x^{2} + 5 x - 1

are x=-1,

\frac{1}{6}

The roots of

4 x^{2} + 4 x - 4

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

x = \frac{- 4 \pm \sqrt{16 + 64}}{8}

x = \frac{- 4 + \sqrt{80}}{8}

x = \frac{- 4 \pm 4 \sqrt{5}}{8}

x = - \frac{1}{2} + \frac{\sqrt{5}}{2}, - \frac{1}{2} - \frac{\sqrt{5}}{2}

The roots of

4 x^{2} + 4 x - 4

are

x = - \frac{1}{2} + \frac{\sqrt{5}}{2}, - \frac{1}{2} - \frac{\sqrt{5}}{2}

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