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Mathematics

Solve the following equation using the formula :

2x2 + 7x + 5 = 0

Quadratic Equations

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Answer

Comparing 2x2 + 7x + 5 = 0 with ax2 + bx + c = 0 we get,

a = 2, b = 7, c = 5.

We know that,

x = −b±b2−4ac2a\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Substituting values we get,

⇒x=−(7)±(7)2−4(2)(5)2(2)=−7±49−404=−7±94=−7±34=−7+34 or −7−34=−44 or −104=−1 or −224=−1 or −212.\Rightarrow x = \dfrac{-(7) \pm \sqrt{(7)^2 - 4(2)(5)}}{2(2)} \\[1em] = \dfrac{-7 \pm \sqrt{49 - 40}}{4} \\[1em] = \dfrac{-7 \pm \sqrt{9}}{4} \\[1em] = \dfrac{-7 \pm 3}{4} \\[1em] = \dfrac{-7 + 3}{4} \text{ or } \dfrac{-7 - 3}{4} \\[1em] = -\dfrac{4}{4} \text{ or } -\dfrac{10}{4} \\[1em] = -1 \text{ or } -2\dfrac{2}{4} \\[1em] = -1 \text{ or } -2\dfrac{1}{2}.

Hence, x = −1,−212-1, -2\dfrac{1}{2}.

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