Question

Solve the quadratic equation by formula: 2x²+11x+5=0​

Answer 1

How to solve your problem

2

2

+

1

1

+

5

=

0

2x^{2}+11x+5=0

2x2+11x+5=0

Quadratic formula

Factor

1

Use the quadratic formula

=

−

±

2

−

4

√

2

x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}

x=2a−b±b2−4ac

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

2

2

+

1

1

+

5

=

0

2x^{2}+11x+5=0

2x2+11x+5=0

=

2

a={\color{#c92786}{2}}

a=2

=

1

1

b={\color{#e8710a}{11}}

b=11

=

5

c={\color{#129eaf}{5}}

c=5

=

−

1

1

±

1

1

2

−

4

⋅

2

⋅

5

√

2

⋅

2

x=\frac{-{\color{#e8710a}{11}} \pm \sqrt{{\color{#e8710a}{11}}^{2}-4 \cdot {\color{#c92786}{2}} \cdot {\color{#129eaf}{5}}}}{2 \cdot {\color{#c92786}{2}}}

x=2⋅2−11±112−4⋅2⋅5

2

Answer 2

Answer:

By middle term splitting,

$2x²+11x+5=0$

$2x²+10x + x+5=0$

$2x(x + 5) + 1(x + 5) = 0$

$(2x + 1) = 0$

$( x + 5) = 0$

$- \frac{1}{2} \: \: \:$

$- 5$

hence the roots are -1/2 and -5