find the roots of the quadratic equations 2x²+x-4=0.
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find the roots of the quadratic equations 2x²+x-4=0.
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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
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Verified answer
Given quadratic equation ,
* 2x² + x - 4 = 0
~ Comparing this equation to ax² + bx + c = 0 , a≠0 , we get ,
{ Now we are going to find the roots by using quadratic formula }
[tex] \large \color{red} \bold{x \: = \frac{ - ( - b)± \sqrt{ {b}^{2} - 4ca} }{2a} }[/tex]
~ Substituting the values ,
[tex] \large \color{blue} \bold{x \: = \frac{ - ( - 1)± \sqrt{ {1}^{2} - 4 \times ( - 4) \times 2} }{2 \times 2} }[/tex]
[tex] \large \color{blue} \bold{ \: \: \: \: \: = \frac{ 1 \: ± \sqrt{ {1} + 32} }{4} }[/tex]
[tex]\large \color{blue} \bold{ \: \: \: \: \: = \frac{ 1 \: ± \sqrt{ 33} }{4} }[/tex]
[tex]\large \color{blue} \bold{ \: \: \: \: \: = \frac{ 1 \: + \sqrt{ 33} }{4} }\large \color{blue} \bold{ \: \: \: \: ,\: \frac{ 1 \: - \sqrt{ 33} }{4} }[/tex]
★ So the roots are →
[tex] \underbrace{\large \color{orange} \bold{ \: \: \: \: \: \frac{ 1 \: + \sqrt{ 33} }{4} }\large \color{green} \bold{ \: \: \: \: and \: \: \: \: \color{indigo}{\frac{ 1 \: - \sqrt{ 33} }{4} }}}[/tex]