Question

Solve the quadratic equation 2x² – 7x + 3 = 0 by using quadratic formula.​

Answer 1

$\huge\underline\mathrm{SOLUTION:-}$

2x² - 7x + 3 = 0

On comparing the given equation with ax² + bx + c = 0, we get,

a = 2, b = -7 and c = 3

By using quadratic formula, we get,

x = [-b±√(b² – 4ac)]/2a

⇒ x = [7±√(49 – 24)]/4

⇒ x = [7±√25]/4

⇒ x = [7±5]/4

Therefore:

⇒ x = 7+5/4 or x = 7-5/4

⇒ x = 12/4 or 2/4

• ∴ x = 3 or ½

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Answer 2

$\sf\large{x = 3 \: and \: \frac{1}{2} }$

Step-by-step explanation:

$\bf\huge {2x}^{2} - 7x + 3 \\ \\ \sf\underline{using \: quadratic \:formula \mapsto: } \\ \sf\boxed{ x = \frac{ - b . \sqrt{ {b}^{2} - 4ac} }{2a}} \\ \\ \tt\ \therefore \: now \: \: {2x}^{2} - 7x + 3 \\ \\ \sf\ x \implies: \frac{ - ( - 7). \sqrt{ {( - 7)}^{2} - 4 \times 2 \times 3} }{2 \times 2} \\ \\\sf\ x \implies: \frac{7. \sqrt{49 - 24} }{4} \\ \\ \sf\ x \implies: \frac{7. \sqrt{25} }{4} \\ \\\sf\ x \implies: \frac{7.5}{4} \\ \\ \boxed{\tt{now}} \\ \\ \bf\ x = \frac{7 + 5}{4} \: \: \: or \: \: \: \frac{7 - 5}{4} \\ \\ \sf\ \implies x = \frac{12}{4} \: \: \: \: \: \: \: \: \: \: \: x\implies\frac{2}{4} \\ \\ \boxed{\sf\ \implies x = 3} \: \: \: \: \: \: \: \: \boxed{x\implies \frac{1}{2} }$