Question

2x^2 + √7x -7 = 0
solve equation using quadratic formula​

Answer 1

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Answer 2

GIVEN :-

• 2x² + √7x - 7 = 0

TO FIND :-

• Roots by using Quadratic Formula.

TO KNOW :-

Quadratic Formula ,

$\\ \bigstar\boxed{\sf \: roots = \dfrac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} }$

Here , a is coefficient of x².

b is coefficient of x.

c is constant.

SOLUTION :

The equation, 2x² + √7x - 7 is in the form ax² + bx + c

So,

• a = 2
• b = √7
• c = -7

Putting values in formula ,

$\\ \sf \: roots = \dfrac{ - \sqrt{7} ± \sqrt{ { (\sqrt{7}) }^{2} - 4(2)( -7 ) } }{2(2)} \\ \\ \\ \sf \: roots = \dfrac{ - \sqrt{7}± \sqrt{7 + 56} }{4} \\ \\ \\ \sf \: roots = \dfrac{ - \sqrt{7} ± \sqrt{63} }{4} \\ \\ \\ \sf \: roots = \dfrac{ - \sqrt{7}±3 \sqrt{7} }{4} \\ \\ \\ \sf \: roots = \dfrac{ - \sqrt{7} + 3 \sqrt{7} }{4} , \dfrac{ - \sqrt{7} - 3 \sqrt{7} }{4} \\ \\ \\ \sf \: roots = \dfrac{2 \sqrt{7} }{4} , \dfrac{ - 4 \sqrt{7} }{4} \\ \\ \\ \underline{\underline{\boxed{\sf \: roots = \dfrac{ \sqrt{7} }{2} , - \sqrt{7} }}}$

Hence , roots are √7/2 , -√7.