Question

find the roots of the quadratic equations 2x²+x-4=0.
​

Answer 1

Answer:

2x

2

+x−4=0

Compairing with ax

2

+bx+c=0

a = 2 b = 1 c = -4

∴

2a

−b±

b

2

−4ac

=

2×2

−1±

1

2

−4×2(−4)

4

−1±

33

∴x=

4

−1+

33

OR x=

4

−1−

33

this is your answer

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Answer 2

Given quadratic equation ,

* 2x² + x - 4 = 0

~ Comparing this equation to ax² + bx + c = 0 , a≠0 , we get ,

• a = 2
• b = 1
• c = -4

{ Now we are going to find the roots by using quadratic formula }

$\large \color{red} \bold{x \: = \frac{ - ( - b)± \sqrt{ {b}^{2} - 4ca} }{2a} }$

~ Substituting the values ,

$\large \color{blue} \bold{x \: = \frac{ - ( - 1)± \sqrt{ {1}^{2} - 4 \times ( - 4) \times 2} }{2 \times 2} }$

$\large \color{blue} \bold{ \: \: \: \: \: = \frac{ 1 \: ± \sqrt{ {1} + 32} }{4} }$

$\large \color{blue} \bold{ \: \: \: \: \: = \frac{ 1 \: ± \sqrt{ 33} }{4} }$

$\large \color{blue} \bold{ \: \: \: \: \: = \frac{ 1 \: + \sqrt{ 33} }{4} }\large \color{blue} \bold{ \: \: \: \: ,\: \frac{ 1 \: - \sqrt{ 33} }{4} }$

★ So the roots are →

$\underbrace{\large \color{orange} \bold{ \: \: \: \: \: \frac{ 1 \: + \sqrt{ 33} }{4} }\large \color{green} \bold{ \: \: \: \: and \: \: \: \: \color{indigo}{\frac{ 1 \: - \sqrt{ 33} }{4} }}}$