Question

Solve by formula method: 2x² – 8x + 4 = 0​

Answer 1

To solve :

• $\sf{2x^{2}-8x+4~~using~quadratic~formula}$

Solution :

Quadratic formula :-

• $\underline{ \boxed{ \sf{ \pmb{ \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }}}}$

　

• a = 2
• b = –8
• c = 4

$\sf{Discriminant,~D=b^{2}-4ac}$

$\sf\implies{(-8)^{2}-4(2)(4)}$

$\sf\implies{64-4(8)}$

$\sf\implies{64-32}$

$\sf{~~~~~ \therefore~{\purple{\underline{\boxed{\sf{\pmb{Discriminant,~b^{2}-4ac=32}}}}}}}$

$\sf\implies{ {\dfrac{-(-8) \pm {\sqrt{32}}}{2(2)}}}$

$\sf\implies{ {\dfrac{8 \pm {\sqrt{16 \times 2}}}{4}}}$

$\sf\implies{ {\dfrac{8 \pm 4{\sqrt{2}}}{4}}}$

$\sf\implies{ {\dfrac{8 + 4{\sqrt{2}}}{4}}~,~~{\dfrac{8 - 4{\sqrt{2}}}{4}}}$

$\sf\implies{ {\purple{\underline{\boxed{\sf{\pmb{2+4{\sqrt{2}}~,~~2-4{\sqrt{2}}}}}}}}}$

∴ Required answer :

Roots are :

• $\sf{{\purple{\pmb{2+4{\sqrt{2}}}}}~~and~~{\purple{\pmb{2-4{\sqrt{2}}}}}}$

Answer 2

TO SOLVE:-

2x² - 8x + 4

FORMULA USED:-

$\frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a}$

SOLUTION:-

D = b² - 4ac

D = (-8)² - 4 × 2 × 4

D = 64 - 32

=> - (-8) + √32/2×2

=> 8 + √16×2/4

=> 8 + 4√2/4 & 8 - 4√2/4

=> 2 + 4√2 & 2 - 4√2

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