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Mathematics

Solve the following equation using the formula :

x2 - 10x + 21 = 0

Quadratic Equations

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Answer

Comparing x2 - 10x + 21 = 0 with ax2 + bx + c = 0 we get,

a = 1, b = -10, c = 21.

We know that,

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

Substituting values we get,

⇒x=−(−10)±(−10)2−4(1)(21)2(1)=10±100−842=10±162=10+162 or 10−162=10+42 or 10−42=142 or 62=7 or 3.\Rightarrow x = \dfrac{-(-10) \pm \sqrt{(-10)^2 - 4(1)(21)}}{2(1)} \\[1em] = \dfrac{10 \pm \sqrt{100 - 84}}{2} \\[1em] = \dfrac{10 \pm \sqrt{16}}{2} \\[1em] = \dfrac{10 + \sqrt{16}}{2} \text{ or } \dfrac{10 - \sqrt{16}}{2} \\[1em] = \dfrac{10 + 4}{2} \text{ or } \dfrac{10 - 4}{2} \\[1em] = \dfrac{14}{2} \text{ or } \dfrac{6}{2} \\[1em] = 7 \text{ or } 3.

Hence, x = 3, 7.

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